Question

lf the midpoint of the line segment joining (3,4) and (k,7) lies on 2x+2y=1, find the value of k.

Answer 1

Using midpoint formula , the coordinates of the midpoint

of the line segment joining (3,4) and (k,7) is

$(\frac{3+k}{2},\frac{4+7}{2})=(\frac{3+k}{2},\frac{11}{2})$

Since the midpoint lie on 2x+2y=1 ---(1)

substituting $x=\frac{3+k}{2}$ and $y=\frac{11}{2}$ in (1), we get

$2\left(\frac{3+k}{2}\right)+2\left(\frac{11}{2}\right)=1$

$\Rightarrow 3+k+11=1$

$\Rightarrow k+14=1$

$\Rightarrow k=1-14$

$\Rightarrow k=-13$