Question

The points a(0,3), b(-2,a) and c(-1,4) are the vertices of rtriangle abc right angled at

a. Find the value of a

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

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Answer 2

Slope of ab= (3-a)/(0-(-2)) = 3-a/2
Slope of bc= (4-a)/(-1-(-2)) = (4-a)
Slope of ca = 4/-1 = -4
Product of a slope of lines perpendicular to each other is -1.
So, (3-a)/2 x -4 = -1
a=2.5