Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 9th

# A(−1, 1), B(1, 3) and C(3, a) are point and if AB = BC, then find ‘a’ - Mathematics

Sum

A(−1, 1), B(1, 3) and C(3, a) are point and if AB = BC, then find ‘a’

#### 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.

Concept: Co-ordinates of Points and Distance
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#### APPEARS IN

Samacheer Kalvi Mathematics Class 9th Tamil Nadu State Board
Chapter 5 Coordinate Geometry
Exercise 5.2 | Q 7 | Page 203