Exercise 1

The triangle OAB is reflected in the origin O to triangle OA’B’. A’ and B’ have coordinates

    \[\left( \text{ }\mathbf{3},\text{ }\text{ }\mathbf{4} \right)\text{ }\mathbf{and}\text{ }\left( \mathbf{0},\text{ }\text{ }\mathbf{5} \right)\]

respectively. (v) Find the co-ordinates of B”, the reflection of B in the x-axis followed by reflection in the origin.

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{...

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The triangle OAB is reflected in the origin O to triangle OA’B’. A’ and B’ have coordinates

    \[\left( \text{ }\mathbf{3},\text{ }\text{ }\mathbf{4} \right)\text{ }\mathbf{and}\text{ }\left( \mathbf{0},\text{ }\text{ }\mathbf{5} \right)\]

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{...

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The triangle OAB is reflected in the origin O to triangle OA’B’. A’ and B’ have coordinates

    \[\left( \text{ }\mathbf{3},\text{ }\text{ }\mathbf{4} \right)\text{ }\mathbf{and}\text{ }\left( \mathbf{0},\text{ }\text{ }\mathbf{5} \right)\]

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{...

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The points

    \[\mathbf{A}\text{ }\left( \mathbf{4},\text{ }\text{ }\mathbf{11} \right),\text{ }\mathbf{B}\text{ }\left( \mathbf{5},\text{ }\mathbf{3} \right),\text{ }\mathbf{C}\text{ }\left( \mathbf{2},\text{ }\mathbf{15} \right),\text{ }\mathbf{and}\text{ }\mathbf{D}\text{ }\left( \mathbf{1},\text{ }\mathbf{1} \right)\]

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{...

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Use a graph paper for this question. (Take 10 small divisions =

    \[1\]

unit on both axes). P and Q have co-ordinates

    \[(0,5)\]

and

    \[\left( -2,\text{ }4 \right)\]

. (iii)

    \[(0,k)\]

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(...

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Use a graph paper for this question. (Take 10 small divisions =

    \[1\]

unit on both axes). P and Q have co-ordinates

    \[(0,5)\]

and

    \[\left( -2,\text{ }4 \right)\]

. (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...

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Use graph paper for this question. (i) The point P

    \[(2,-4)\]

is reflected about the line x =

    \[0\]

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 = \[0\],...

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Use a graph sheet for this question. Take

    \[1\]

cm =

    \[1\]

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’,...

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Use graph paper for this (take

    \[2\]

cm =

    \[1\]

unit along both x and y-axis). ABCD is a quadrilateral whose vertices are

    \[\mathbf{A}\text{ }\left( \mathbf{2},\text{ }\mathbf{2} \right),\text{ }\mathbf{B}\text{ }\left( \mathbf{2},\text{ }-\mathbf{2} \right),\text{ }\mathbf{C}\text{ }\left( \mathbf{0},\text{ }-\mathbf{1} \right)\]

and

    \[~\mathbf{D}\text{ }\left( \mathbf{0},\text{ }\mathbf{1} \right)\]

. (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,...

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The point

    \[(-3,0)\]

on reflection in a line is mapped as

    \[(3,0)\]

and the point

    \[(2,-3)\]

on reflection in the same line is mapped as

    \[(-2,-3)\]

. (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...

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The triangle ABC where

    \[\mathbf{A}\text{ }\left( \mathbf{1},\text{ }\mathbf{2} \right),\text{ }\mathbf{B}\text{ }\left( \mathbf{4},\text{ }\mathbf{8} \right),\text{ }\mathbf{C}\text{ }\left( \mathbf{6},\text{ }\mathbf{8} \right)\]

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}...

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(i) Point P (a, b) is reflected in the x-axis to P’

    \[(5,-2)\]

. 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,...

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