According to the question, ∆ OAB is reflected in the origin O to ∆ OA’B’, And the co-ordinates of \[A\text{ }=\text{ }\left( -3,\text{ }-4 \right)\text{ }and\text{ }B\text{ }=\text{ }\left( 0,\text{...
The triangle OAB is reflected in the origin O to triangle OA’B’. A’ and B’ have coordinates
The triangle OAB is reflected in the origin O to triangle OA’B’. A’ and B’ have coordinates
respectively. (iii) What kind of figure is the quadrilateral ABA’B’? (iv) Find the coordinates of A”, the reflection of A in the origin followed by reflection in the y-axis.
According to the question, ∆ OAB is reflected in the origin O to ∆ OA’B’, And the co-ordinates of \[A\text{ }=\text{ }\left( -3,\text{ }-4 \right)\text{ }and\text{ }B\text{ }=\text{ }\left( 0,\text{...
The triangle OAB is reflected in the origin O to triangle OA’B’. A’ and B’ have coordinates
respectively. (i) Find the co-ordinates of A and B. (ii) Draw a diagram to represent the According to the question information.
According to the question, ∆ OAB is reflected in the origin O to ∆ OA’B’, And the co-ordinates of \[A\text{ }=\text{ }\left( -3,\text{ }-4 \right)\text{ }and\text{ }B\text{ }=\text{ }\left( 0,\text{...
Use a graph paper for this question (take
cm =
unit on both x and y axes). (iii) Join points A, B, C, D, D’, C’, B’ and A in order, so as to form a closed figure. Write down the equation of line of symmetry of the figure formed.
(iii) The points A, B, C, D, D’, C’, B’ and A in order to form a closed figure. Hence, the equation of the line of symmetry is x = \[0\]
The points
are the vertices of a parallelogram. If the parallelogram is reflected in the y-axis and then in the origin, find the co-ordinates of the final images. Check whether it remains a parallelogram. Write down a single transformation that brings the above change.
According to the question, points \[\mathbf{A}\text{ }\left( \mathbf{4},\text{ }\text{ }\mathbf{11} \right),\text{ }\mathbf{B}\text{ }\left( \mathbf{5},\text{ }\mathbf{3} \right),\text{...
are the vertices of a triangle. ∆ ABC is reflected in the y-axis and then reflected in the origin. Find the co-ordinates of the final images of the vertices.
According to the question, \[\mathbf{A}\text{ }\left( \mathbf{4},\text{ }\text{ }\mathbf{1} \right),\text{ }\mathbf{B}\text{ }\left( \mathbf{0},\text{ }\mathbf{7} \right)\text{ }\mathbf{and}\text{...
A point P (a, b) becomes
after reflection in the x-axis, and P becomes (d, 5) after reflection in the origin. Find the values of a, b, c and d.
According to the question, point P (a, b) and the image of P (a, b) after reflected in the x-axis be (a, -b) But it is According to the question as \[(-2,c)\] Thus, \[a\text{ }=\text{ }-2,\text{...
The point P (a, b) is first reflected in the origin and then reflected in the y-axis to P’. If P’ has co-ordinates
,evaluate a, b
The co-ordinates of image of P (a, b) reflected in origin are (-a, -b). Again, the co-ordinates of P’ which is image of the above point (-a, -b) reflected in the y-axis are (a, -b). But the...
The point P
on reflection in x-axis is mapped onto P’. Then P’ on reflection in the y-axis is mapped onto P”. Find the co-ordinates of P’ and P”. Write down a single transformation that maps P onto P”.
According to the question, P’ is the image of P \[\left( \mathbf{4},\text{ }\text{ }\mathbf{7} \right)\] reflected in x-axis Thus, the co-ordinates of P’ are \[\left( 4,\text{ }7 \right)~\] Again P”...
Use a graph paper for this question. (Take 10 small divisions =
unit on both axes). P and Q have co-ordinates
and
. (iii)
on reflection in the origin is invariant. Write the value of k. (iv) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by a reflection in x-axis.
According to the question:, two points P \[(0,5)\] and Q \[\left( -2,\text{ }4 \right)\] (iii) \[(0,k)\] on reflection in the origin is invariant. So, the co-ordinates of image will be \[\left(...
Use a graph paper for this question. (Take 10 small divisions =
unit on both axes). P and Q have co-ordinates
and
. (i) P is invariant when reflected in an axis. Name the axis. (ii) Find the image of Q on reflection in the axis found in (i).
According to the question:, two points P \[(0,5)\] and Q \[\left( -2,\text{ }4 \right)\] (i) As the abscissa of P is \[0\]. It is invariant when is reflected in y-axis. (ii) Let Q’ be the image of Q...
The point P
is reflected to P’ in the x-axis and O’ is the image of O (origin) in the line PP’. Find: (iii) the perimeter of the quadrilateral POP’O’.
According to the question:, P’ is the image of P\[(3,4)\] reflected in x- axis and O’ is the image of O the origin in the line P’P. (iii) Perimeter of POP’O’ is (\[4\]x OP) units. Let Q be the point...
The point P
is reflected to P’ in the x-axis and O’ is the image of O (origin) in the line PP’. Find: (iii) the perimeter of the quadrilateral POP’O’. Solution:
According to the question:, P’ is the image of P\[(3,4)\] reflected in x- axis and O’ is the image of O the origin in the line P’P. (i) Hence, co-ordinates of P’ are \[(3,-4)\] and co-ordinates of...
The point P
is reflected to P’ in the x-axis and O’ is the image of O (origin) in the line PP’. Find: (i) the co-ordinates of P’ and O’, (ii) the length of segments PP’ and OO’.
According to the question:, P’ is the image of P\[(3,4)\] reflected in x- axis and O’ is the image of O the origin in the line P’P. (i) Hence, co-ordinates of P’ are \[(3,-4)\] and co-ordinates of...
The points
are the vertices of ∆ABC. (iii) Assign the special name to the quadrilateral
and find its area.
According to the question:, points \[\mathbf{A}\text{ }\left( \mathbf{2},\text{ }\mathbf{3} \right),\text{ }\mathbf{B}\text{ }\left( \mathbf{4},\text{ }\mathbf{5} \right)\text{ }\mathbf{and}\text{...
The points
are the vertices of ∆ABC. (i) Write down the co-ordinates of
if
is the image of ∆ ABC when reflected in the origin. (ii) Write down the co-ordinates of
if
is the image of ∆ ABC when reflected in the x-axis.
Use graph paper to answer this question (iii) If B’ is the image of B when B is reflected in the line AA’, write the co-ordinates of B’. (iv) Give the geometrical name for the figure ABA’B’.
(iii) The co-ordinates of the image of B when reflected in the line AA’ are B’ = \[(7,2)\] (iv) It’s seen that in the quadrilateral ABA’B’, we have AB = AB’ and A’B = A’B’ Thus, ABA’B’ is a...
Use graph paper to answer this question (i) Plot the points A
and B
. (ii) If A’ is the image of A when reflected in x-axis, write the co-ordinates of A’.
(i) Plotting the points A \[(4,6)\] and B \[(1,2)\] on the According to the question: graph. (ii) The co-ordinates of the image of A when reflected in axis are A’\[(4,-6)\]
Using a graph paper, plot the points A
and B
. (iii) State the geometrical name for the figure ABA’B’. (iv) Find its perimeter.
Points A \[(6,4)\] and B\[(0,4)\] are plotted on a graph paper. (iii) The geometrical name for ABA’B’ is parallelogram (iv) From the figure in graph paper, we see that Length of AB = A’B’ = \[6\]...
Using a graph paper, plot the points A
and B
. (i) Reflect A and B in the origin to get the images A’ and B’. (ii) Write the co-ordinates of A’ and B’.
Points A \[(6,4)\] and B\[(0,4)\] are plotted on a graph paper. (i) A and B are reflected in the origin to get images A’ and B’ (ii) Hence, The co-ordinates of A’ are \[(-6,-4)\] The co-ordinates of...
Use graph paper for this question. (iii) Name the figure PQR. (iv) Find the area of figure PQR.
(iii) Figure PQR is the right-angled triangle PQR. (iv) Area of ∆ PQR = \[1/2\] x QR x PQ \[=~1/2\times \text{ }4\text{ }\times \text{ }8~\] = \[16\] sq. units.
Use graph paper for this question. (i) The point P
is reflected about the line x =
to get the image Q. Find the co-ordinates of Q. (ii) Point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.
(i) As the point Q is the reflection of the point P\[(2,-4)\] in the line x = \[0\], Thus, the co-ordinates of Q are \[(2,4)\]. (ii) As R is the reflection of Q \[(2,4)\] about the line y = \[0\],...
Use a graph sheet for this question. Take
cm =
unit along both x and y-axis. (iii) Write down the coordinates of B’, C’ and D’. (iv) Join the points A, B, C, D, D’, C’, B’, A in order and give a name to the closed figure ABCDD’C’B’.
(iii) The coordinates of B’ are \[\left( -3,\text{ }0 \right),\text{ }C\text{ }\left( -1,\text{ }0 \right)\text{ }and\text{ }D\text{ }\left( -1,\text{ }-5 \right)\] (iv) Points A, B, C, D, D’, C’,...
Use a graph sheet for this question. Take
cm =
unit along both x and y-axis. (i) Plot the point:
(ii) Reflect the points B, C and D on the y-axis and name them as B’, C’ and D’ respectively.
(i) Points \[\mathbf{A}\text{ }\left( \mathbf{0},\text{ }\mathbf{5} \right),\text{ }\mathbf{B}\text{ }\left( \mathbf{3},\text{ }\mathbf{0} \right),\text{ }\mathbf{C}\text{ }\left( \mathbf{1},\text{...
Use graph paper for this (take
cm =
unit along both x and y-axis). ABCD is a quadrilateral whose vertices are
and
. (iii) Name two points which are invariant under the above reflection. (iv) Name the polygon A’B’CD.
(iii) Points C \[(0,-1)\] and D \[(0,1)\] are invariant under the above reflection. (iv) The polygon A’B’CD is a trapezium since A’B’ || CD.
Use graph paper for this (take
cm =
unit along both x and y-axis). ABCD is a quadrilateral whose vertices are
and
. (i) Reflect quadrilateral ABCD on the y-axis and name it as A’B’CD. (ii) Write down the coordinates of A’ and B’.
(i) Quadrilateral ABCD is reflected on the y-axis and named as A’B’CD. (ii) As A’ is the reflection of \[A(2,2)\] about the line x = \[0\] (y-axis) Thus, the co-ordinates of A’ are \[(-2,2)\]. And,...
The point
on reflection in a line is mapped as
and the point
on reflection in the same line is mapped as
. (i) Name the mirror line. (ii) Write the co-ordinates of the image of (-3, -4) in the mirror line.
According to the question:, The point is the image of point \[(3,0)\] and point \[(2,-3)\] is image of point \[(-2,-3)\] reflected on the same line. (i) Clearly, it’s seen that the mirror line...
Given two points P and Q, and that (1) the image of P on reflection in the y-axis is the point Q and (2) the midpoint of PQ is invariant on reflection in x-axis. Locate: (iii) the origin.
According to the question:, Q is the image of P on reflection in y-axis and mid-point of PQ is invariant on reflection in x-axis (iii) The origin will be the mid-point of line segment PQ.
Given two points P and Q, and that (1) the image of P on reflection in the y-axis is the point Q and (2) the midpoint of PQ is invariant on reflection in x-axis. Locate: (i) the x-axis (ii) the y-axis and
According to the question:, Q is the image of P on reflection in y-axis and mid-point of PQ is invariant on reflection in x-axis (i) x-axis will be the line joining the points P and Q. (ii) The line...
The image of a point P on reflection in a line l is point P’. Describe the location of the line l.
The line will be the right bisector of the line segment joining P and P’.
The triangle ABC where
is reflected in the x-axis to triangle A’ B’ C’. The triangle A’ B’ C’ is then reflected in.the origin to triangle A”B”C” Write down the co-ordinates of A”, B”, C”. Write down a single transformation that maps ABC onto A” B” C”.
According to the question:, The co-ordinates of ∆ ABC are \[\mathbf{A}\text{ }\left( \mathbf{1},\text{ }\mathbf{2} \right),\text{ }\mathbf{B}\text{ }\left( \mathbf{4},\text{ }\mathbf{8}...
The points
,
and
are the vertices of a right-angled triangle. Check whether it remains a right-angled triangle after reflection in the y-axis.
Let A \[(6,2)\], B \[(3,-1)\] and C \[(-2,4)\] be the points of a right-angled triangle Then, The co-ordinates of the images of A, B, C reflected in y-axis will be: A’\[(-6,2)\], B’\[(-3,-1)\] and...
Plot the points A
, B
and C
on the graph paper. Draw the triangle formed by reflecting these points in the x-axis. Are the two triangles congruent?
The points A \[(2,-3)\], B \[(-1,2)\] and C\[(0,-2)\] has been plotted on the graph paper as shown and are joined to form a triangle ABC. Hence, the co-ordinates of the images of A, B and C...
Points A and B have co-ordinates
and
. Find (i) the image A’ of A under reflection in the x-axis. (ii) the image B’ of B under reflection in the line AA’.
According to the question:, co-ordinates of A are \[(2,5)\] and of B are \[(0,3)\] (i) Co-ordinates of A’, the image of A reflected in the x-axis will be \[(2,-5)\] (ii) Co-ordinates of B’, the...
(i) Point P (a, b) is reflected in the x-axis to P’
. Write down the values of a and b. (ii) P” is the image of P when reflected in the y-axis. Write down the co-ordinates of P”. (iii) Name a single transformation that maps P’ to P”.
(i) Image of P (a, b) reflected in the x-axis to P’ \[(5,-2)\] So, the co-ordinates of P will be \[(5,2)\] Hence, a =\[5\] and b = \[2\] (ii) P” is the image of P when reflected in the y-axis Thus,...
If P’
is the image of a point P under reflection in the origin, find (i) the co-ordinates of P. (ii) the co-ordinates of the image of P under reflection in the line y =
.
(i) According to the question:, reflection of P is P’ \[\left( -\mathbf{4},\text{ }-\mathbf{3} \right)\] in the origin Thus, the co-ordinates of P will be \[\left( 4,\text{ }3 \right)\] Now, Draw a...
Find the co-ordinates of the image of
under reflection in x-axis followed by a reflection in the line x =
.
The steps for finding the co-ordinates are as follows: (i) Draw axis XOX’ and YOY’ taking \[1\] cm = \[1\] unit. (ii) Plot a point P \[(3,1)\]. (iii) Draw a line x = \[1\], which is parallel to...
Write down the co-ordinates of the image of the point
when: (iii) reflected in the x-axis followed by a reflection in the y-axis (iv) reflected in the origin.
The co-ordinates of the According to the question: point are \[(3,-2)\]. Now, (iii) Co-ordinates of the point reflected in x- axis followed by reflection in the y-axis will be \[\left( -3,\text{ }2...
The point P
on reflection in y-axis is mapped on P’. The point P’ on reflection in the origin is mapped on P”. Find the co-ordinates of P’ and P”. Write down a single transformation that maps P onto P”.
According to the question:, point P \[\left( -4,\text{ }-5 \right)\] And, P’ is the image of point P in y-axis Thus, the co-ordinates of P’ will be \[(4,-5)\] Again, P” is the image of P’ under...
(i) The point P
on reflection in the line y =
is mapped onto P’ Find the co-ordinates of P’. (ii) Find the image of the point P
in the line y = -2.
(i) The steps for finding the co-ordinates are: (a) Draw axis XOX’ and YOY’ and take \[1\] cm = \[1\] unit. (b) Plot point P \[\left( \mathbf{2},\text{ }\mathbf{4} \right)\] on it. (c) Draw a line y...
(i) The point P
is reflected in the line x =
to the point P’. Find the co-ordinates of the point P’. (ii) Find the image of the point P
in the line x =
(i) The steps for finding the co-ordinates of the point P’ are: (a) Draw axis XOX’ and YOY’ and take \[1\] cm = \[1\] unit (b) Plot point P \[(2,3)\] on it. (c) Draw a line x = \[4\] which is...
A point P is reflected in the origin. Co-ordinates of its image are
. Find (i) the co-ordinates of P. (ii) the co-ordinates of the image of P in the x-axis.
The co-ordinates of image of a point P which is reflected in origin are \[\left( \mathbf{2},\text{ }-\mathbf{5} \right)\], then (i) Co-ordinates of P will be \[\left( -2,\text{ }5 \right)\] (ii)...
A point P is reflected in the x-axis. Co-ordinates of its image are
. (i) Find the co-ordinates of P. (ii) Find the co-ordinates of the image of P under reflection in the y-axis.
(i) we got the co-ordinates of image of P which is reflected in x-axis are \[(8,-6)\] (ii) we got the co-ordinates of image of P under reflection in the y-axis will be \[(-8,6)\]
The image of a point P under reflection in the x-axis is
.Write down the coordinates of P.
According to the question: that \[\left( \mathbf{5},\text{ }-\mathbf{2} \right)\] are the co-ordinates of the image of a point P under x-axis Thus, the co-ordinates of P will be \[\left(...
Find the co-ordinates of the images of the following points under reflection in the origin: (iii)
the co-ordinates of the images of the following points under reflection in the origin: Image of \[\left( \mathbf{0},\text{ }\mathbf{0} \right)\] will be \[\left( \mathbf{0},\text{ }\mathbf{0}...
Find the co-ordinates of the images of the following points under reflection in the origin: (i)
(ii)
The co-ordinate of the image of the following points under reflection in the y-axis will be: (i) Image of \[\left( \mathbf{2},\text{ }-\mathbf{5} \right)\] will be \[\left( -2,\text{ }5 \right)\]...
Find the co-ordinates of the images of the following points under reflection in the x- axis:
The co-ordinates of the images of the points under reflection in the x-axis will be: Image of \[\left( -\mathbf{7},\text{ }\mathbf{0} \right)\] will be \[\left( -\mathbf{7},\text{ }\mathbf{0}...
Find the co-ordinates of the images of the following points under reflection in the y-axis:
The co-ordinates of the image of the points under reflection in the y-axis will be: Image of \[\left( -3/2,\text{ }1/2 \right)\]will be \[\left( -3/2,\text{ }1/2 \right)\]
Find the co-ordinates of the images of the following points under reflection in the y-axis:
The co-ordinates of the image of the points under reflection in the y-axis will be: Image of \[\left( \mathbf{2},\text{ }-\mathbf{5} \right)\] will be \[\left( -2,\text{ }-5 \right)\]
Find the co-ordinates of the images of the following points under reflection in the x- axis:
The co-ordinates of the images of the points under reflection in the x-axis will be: Image of \[\left( -\mathbf{7},\text{ }\mathbf{0} \right)\] will be \[\left( -\mathbf{7},\text{ }\mathbf{0}...
Find the co-ordinates of the images of the following points under reflection in the x- axis:
The co-ordinates of the images of the points under reflection in the x-axis will be: Image of \[\left( -\mathbf{3}/\mathbf{2},\text{ }-\mathbf{1}/\mathbf{2} \right)\] will be \[\left( -3/2,\text{...
Find the co-ordinates of the images of the following points under reflection in the x- axis:
The co-ordinates of the images of the points under reflection in the x-axis will be: Image of \[\left( \mathbf{2},\text{ }-\mathbf{5} \right)\] will be \[\left( 2,\text{ }5 \right)\]