Question

If (1, 4) is the midpoint of the line joining the points A(-5, 2) and B, then find the coordinates of B.

• A. $(7,6)$
• B. $(6,7)$
• C. $(7,-6)$
• D. $(-7,6)$

Answer 1

The correct option is A $(7,6)$

Given, coordinates of $A\equiv (-5,2)\equiv (x_1,y_1)$
Let the coordinates of B are $(x_2,y_2).$

We know that, the midpoint of the points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

As, $(1,4)$ is the midpoint of $A(-5,2)$ and $B(x_2,y_2)$
$\therefore (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(1,4)$
$\Rightarrow (\frac{-5+x_2}{2},\frac{2+y_2}{2})=(1,4)$

Equating $x$ coordinates, we get
$\frac{-5+x_2}{2}=1$
Multiply both sides by 2
$\frac{-5+x_2}{2}\times 2=1\times 2$
$\Rightarrow -5+x_2=2$
Add 5 to both sides
$-5+x_2+5=2+5\Rightarrow x_2=7$

Similarly, equating $y$ coordinates, we get
$\frac{2+y_2}{2}=4$
$\Rightarrow \frac{2+y_2}{2}\times 2=4\times 2$
$\Rightarrow 2+y_2=8\Rightarrow y_2=8-2=6$

Hence, the coordinates of $B$ are $(7,6).$