Question

In the following figure, F is the midpoint of the line segment GH. Which of the following are the coordinates of F?

• A. $(1,4)$
• B. $(2,5)$
• C. $(\frac{3}{2},4)$
• D. $(\frac{3}{2},\frac{9}{2})$
• E. $(2,\frac{9}{2})$

Answer 1

Answer: (D)

$(\frac{3}{2},\frac{9}{2})$

Given coordinates are $G(-6,1)$ and $H(9,8)$.

To find out,

The coordinates of $F$

Let the coordinates of $F$ be $(x,y)$.

We know that the coordinates of the midpoint of the line segment joining $(x_1,y_1)and(x_2,y_2)$ are:

$P(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Here, $\left(x_{1,}{,y}_1\right)=(9,8)$
and $(x_2,y_2)=(-6,1)$

Hence, $(x,y)=(\frac{9+(-6)}{2},\frac{8+1}{2})$
$=(\frac{3}{2},\frac{9}{2})$

Hence, the coordinates of $F$ are $(\frac{3}{2},\frac{9}{2})$.