Advertisements
Advertisements
प्रश्न
A(−1, 1), B(1, 3) and C(3, a) are point and if AB = BC, then find ‘a’
उत्तर
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((1 + 1)^2 + (3 - 1)^2`
= `sqrt((2)^2 + (2)^2`
= `sqrt(4 + 4)`
= `sqrt(8)`
BC = `sqrt((3 - 1)^2 + ("a" - 3)^2`
= `sqrt((2)^2 + ("a" - 3)^2`
= `sqrt(4 + ("a" - 3)^2`
But given AB = BC
⇒ `sqrt(8) = sqrt(4 + ("a" - 3)^2`
4 + (a – 3)2 = 8
(a – 3)2 = 8 – 4
(a – 3)2 = 4
a – 3 = `sqrt(4)`
= ± 2
a – 3 = 2 or a – 3 = – 2
a = 2 + 3 or a = 3 – 2
a = 5 or a = 1
∴ The value of a = 5 or a = 1.
APPEARS IN
संबंधित प्रश्न
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = 6, y = - 2
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = -3, y = -6
Sketch proper figure and write the answer of the following question.
If X-Y-Z and l(XZ) = `3sqrt7`, l(XY) = `sqrt7`, then l(YZ) = ?
On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.
d(P, Q) + d(Q, R) = d(P, R)
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
- 4, 5
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
x + 3, x - 3
If A-B-C and d(A, C) = 17, d(B, C) = 6.5 then d(A, B) = ?
Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, −4) and (5, −6)
The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.
The point whose ordinate is 4 and which lies on the y-axis is _______________
