Advertisements
Advertisements
Question
A(−1, 1), B(1, 3) and C(3, a) are point and if AB = BC, then find ‘a’
Advertisements
Solution
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
RELATED QUESTIONS
Find the distance with the help of the number line given below.
d (Q, B)
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = 1, y = 7
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 = 4, y = - 8
Co-ordinates of the pair of a point is given below. Hence find the distance between the pair.
3, 6
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
x + 3, x - 3
Verify that the following points taken in order to form the vertices of a rhombus
A(1, 1), B(2, 1), C(2, 2) and D(1, 2)
Find the distance with the help of the number line given below.
d(B, E)
Find the distance with the help of the number line given below.
d(O, E)
Find the distance with the help of the number line given below.
d(P, J)
