Question

The coordinates of P and Q are (2k, 7) and (-k, 4) respectively. Given that the gradient. of the line segment PQ is -2, find the value of k​

Answer 1

SOLUTION

GIVEN

The coordinates of P and Q are (2k, 7) and (-k, 4) respectively. Given that the gradient of the line segment PQ is -2

TO DETERMINE

The value of k

EVALUATION

Here it is given that the coordinates of P and Q are (2k, 7) and (-k, 4) respectively.

The gradient of the line segment PQ is

$\displaystyle\sf{ = \frac{7 - 4}{2k + k} }$

$\displaystyle\sf{ = \frac{3}{3 k} }$

$\displaystyle\sf{ = \frac{1}{ k} }$

By the given condition

$\displaystyle\sf{\frac{1}{ k} = - 2 }$

$\displaystyle\sf{ \implies \: k = - \frac{1}{2} }$

FINAL ANSWER

$\displaystyle\sf{ \: k = - \frac{1}{2} }$

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