Solution: Let the co-ordinates of Q be (x2, y2). Given co-ordinates of P = (-3,2) Co-ordinates of midpoint = (1,-2) Here x1 = -3, y1 = 2 , x = 1 , y = -2 By Midpoint formula, x = (x1+x2)/2 1 =...
Solution: Let the midpoint of line joining the points A(3m,6) and B(-4,3n) be C(1,2m-1). Here x1 = 3m, y1 = 6 , x2 = -4, y2 = 3n x = 1 , y = 2m-1 By Midpoint formula, x = (x1+x2)/2 1 = (3m+-4)/2...
Solution: Given Co-ordinates of A = (-3,1) Co-ordinates of B = (5,-4) Here x1 = -3, y1 = 1 , x2 = 5, y2 = -4 Let C(x,y) be the midpoint of AB By midpoint formula, x = (x1+x2)/2 y = (y1+y2)/2 x =...
(v) In quadrilateral ABC1B1, ABB1C1 Hence the quadrilateral ABC1B1 is a trapezium.
(iii) The quadrilateral ABA1B1 will be a rhombus. (iv) Let C be midpoint of AB. Co-ordinate of C = ((3+0)/2 , (0+4)/2) = (3/2, 2) [Midpoint formula] In a point reflection in the origin, the image of...
(i) Co-ordinates of point A are (3,0). When you reflect a point across the Y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed)...
(iii) Co-ordinates of P’ = (3,5) Co-ordinates of P’’ = (-3,-5) Here x1 = 3, y1 = 5 , x2 = -3, y2 = -5 Let Q(x,y) be the midpoint of P’P’’ By midpoint formula, x = (x1+x2)/2 y = (y1+y2)/2 x =...
Solution: (i) The image of P(3,-5) when reflected in X-axis will be (3,5). When you reflect a point across the X-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its...
Let P be the point which is three-fourth of the way from A(3,1) to B(-2,5). AP/AB = 3/ 4 AB = AP+PB AP/AB = AP/(AP+PB) = 3/4 4AP = 3AP+3PB 4AP-3AP = 3PB AP = 3PB AP/PB = 3/1 The ratio m:n = 3:1 x1 =...
Solution: (i) Let the co-ordinates of P(x, y) divides AB in the ratio m:n. A(3,2) and B(5,1) are the given points. Given m:n = 1:2 x1 = 3 , y1 = 2 , x2 = 5 , y2 = 1 , m = 1 and n = 2 By Section...
Let P and Q be the points of trisection of AB i.e., AP = PQ = QB Given A(3,-3) and B(6,9) x1 = 3, y1 = -3, x2 = 6, y2 = 9 P(x, y) divides AB internally in the ratio 1 : 2. m:n = 1:2 By applying the...
Solution: Let the co-ordinates of P(x, y) divides AB in the ratio m:n. A(-2,1) and B(1,4) are the given points. Given m:n = 2:1 x1 = -2 , y1 = 1 , x2 = 1 , y2 = 4 , m = 2 and n = 1 By Section...
Solution: Let the co-ordinates of P(x, y) divides AB in the ratio m:n. A(-3,3) and B(12,-7) are the given points. Given m:n = 2:3 x1 = -3 , y1 = 3 , x2 = 12 , y2 = -7 , m = 2 and n = 3 By Section...
(iii) Co-ordinates of midpoint of line joining the points (x1,y1) and (x2,y2) = {(x1+x2)/2 ,(y1+y2)/2} Co-ordinates of midpoint of line joining the points (a+3, 5b) and (2a-1,3b+4) = {(a+3+2a-1)/2,...
Solution: Co-ordinates of midpoint of line joining the points (x1,y1) and (x2,y2) = {(x1+x2)/2 ,(y1+y2)/2} (i) Co-ordinates of midpoint of line joining the points (2, -3) and (-6,7) = {(2+-6)/2,...
Solution: (i) In \[\vartriangle CPQ\text{ }and\text{ }\vartriangle CAB\] \[\angle PCQ\text{ }=\angle APQ\] [As PQ || AB, corresponding angles are equal.] \[\angle C\text{ }=\angle C\] [Common angle]...
Let the length of the shadow of the tree to be x meters. Therefore, the height of the tree = √3 x meters If θ is the angle of elevation of the sun, \[\begin{array}{*{35}{l}} =>\text{ }tan\text{...
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According to the question, \[A\text{ }=\text{ }\left\{ 1,\text{ }2,\text{ }3 \right\}\]. (i) Let \[{{R}_{1}}~=\text{ }\left\{ \left( 1,\text{ }1 \right),\text{ }\left( 1,\text{ }2 \right),\text{...
Let take the cost of the entry ticket initially and at present to be 10x and 13x respectively. And let the number of visitors initially and at present be 6y and 5y respectively. Therefore,...
=
passes through the point 
. find the value of kSolution:- From the question it is given that, The line $(3+5y)/2$ =$(4x –7)/3$ passes through the point$ (1, k)$ We have to find the value of k, So, putx =$1$ and y = k $(3+5y)/2 =(4x –7)/3$...
marbles. Both of them lost 
marbles each, and the product of the number of marbles they now have is 
. Form the quadratic equation to find how many marbles they to start with, if John had 
marbles.Solution: Quadratic equations are the polynomial equations of degree $2$ in one variable of type $f(x) = ax2 + bx + c$ where a, b, c, ∈ R and a ≠ 0. Given, John and Jilani...
. Two coins are tossed simultaneously 
times and the outcomes are noted asTwo tails: $83$ One tail: $140$ No tail: $77$ Find the probability of occurrence of each these events. Solution:- the extent to which an event is likely to occur, measured by the ratio of the...
. Take a point P on its circumference. Construct a tangent to the circle at P without using the center.In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length. In math, the circumference...