Question

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

• A. k = -15
• B. k = 5
• C. k = -1
• D. None of these

Answer 1

The correct option is A k = -15

Midpoint 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, $2a+3b=5$
$2\times \frac{(-7+k)}{2}+3\left(9\right)=5$
$-7+k+27=5$
$k=-15$