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Differentiability

If the points...

Question

If the points (0, 4) (4, 0) and (5, P) are collinear, the value of P is

A

- 1

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B

7

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C

6

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D

4

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Solution

The correct option is D $- 1$
The given points (0, 4), (4, 0) and (5, P) are collinear, if
$\frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})] = 0$
$⟹ \frac{1}{2} [0 (0 - P) + 4 (P - 4) + 5 (4 - 0)] = 0$
$⟹ 4 P - 16 + 20 = 0$
$∴ P = - 1$

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