Question

The points A (0, 3), B (-2, a) and C (-1, 4) are the vertices of a right angled triangle
at A, find the value of a.
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Answer 1

Answer:

Length of AB =√[(-2-0)²+(a-3)²]=√4+(a-3)²

Length of BC=√1²+(4-a)²=√1+4-a²

Length of CA=√1²+1²=√2

BC²=AC²+AB²

1+(4-a)²=2+4+(a-3)²

1+16+a²-8a=6+a²+9-6a

17+a²-8a=15+a²-6a

2+a²-a²=-6a+8a

2a=2

a=1