Q. 185.0( 1 Vote )

# The points A(0, 3), B(-2, a) and C(-1, 4) are the vertices of a Î ABC right âangledat A. Find the value of a.

a = 1
SOLUTION:

Given, the vertices of a Δ ABC are right –angled at A.

Using Pythagoras theorem
AB 2 + AC 2 = BC 2
AB 2 = (- 2 - 0) 2 + (a - 3) 2 = 4 + (a – 3) 2
BC 2 = (- 1 + 2) 2 + (4 - a) 2 = 1 + (4 – a) 2
AC 2 = (- 1 - 0) 2 + (4 - 3) 2 = 1 + 1 = 2
Since, AB 2 + AC 2 = BC 2
4 + (a – 3) 2 + 2 = 1 + (4 – a) 2
4 + a 2 + 9 – 6a + 2 = 1 + 16 + a 2 – 8a
2a = 2
a = 1.

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