Question

The mid-point of the line segment joining $(2a,4)$ and $(-2,2b)$ is $(1,2a+1)$. The values of $a$ and $b$ are

• A. $a=b,b=-1$
• B. $a=2,b=-3$
• C. $a=3,b=-2$
• D. $a=2,b=3$

Answer 1

The correct option is D $a=2,b=3$

Midpoint of two points $=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Given, midpoint of $(2a,4)$ and $(-2,2b)=(1,2a+1)$

$=>(\frac{2a-2}{2},\frac{4+2b}{2})=(1,2a+1)$

$=>\frac{2a-2}{2}=1;\frac{4+2b}{2}=2a+1$

$=>2a-2=2$

$=>a=2$

And, $\frac{4+2b}{2}=2a+1$

$=>\frac{4+2b}{2}=2\left(2\right)+1=5$

$=>4+2b=10$

$=>2b=6$

$=>b=3$