Find the value of $k$ if the triangle formed by A $(8, 10)$ , B $(7, 3)$ and C $(0, k)$ is right angled at B.

8

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- 4

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10

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Solution

The correct option is B $- 4$
As B is a right angle, so, AC must be the hypotenuse and hence by
Pythagoras Theorem, AC² = AB² + BC²
Or, (0 – 8)² + (k + 10)² = (7 – 8)2+ (– 3 + 10)² + (0 – 7)² + (k +3)²
Or, 64 + k² + 20k + 100 = 1 + 49 + 49 + k² + 6k + 9
Or, $14 k = 108 - 164 = - 56 O r, k = - \frac{56}{14} = - 4.$ [Ans.]

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