If the mid point of the line-segment joining the points (-7, 14) and (k, 4) is (a, b) where 2a + 3b = 5 then the value of k is

k = 15

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k = -7

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k = -15

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k = 10

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Solution

The correct option is C k = -15
Mid point of two points ${(x}_{1}, y_{1})$ and
${(x}_{2}, y_{2})$ is calculated by the formula $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$
So, mid point of $(- 7, 14); (k, 4) = (a, b)$
$=> (\frac{- 7 + k}{2}, \frac{14 + 4}{2}) = (a, b)$
$=> a = \frac{- 7 + k}{2}; b = 9$
Given, $2 a + 3 b = 5$
$2 \times \frac{(- 7 + k)}{2} + 3 (9) = 5$
$- 7 + k + 27 = 5$
$k = - 15$

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Similar questions

If $(a, b)$ is the mid-point of the line segment joining the points $A (10, 6)$ and $B (k, - 4)$ and $a + 2 b = 18,$ find the value of $k .$

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