Question

The midpoint M of CD has coordinates (2, 5). Point C has coordinates (4, 3). What are the coordinates of point D?

Answer 1

The coordinates of point D is (0, 7)

solution:

The midpoint M of CD has coordinates (2, 5)

Point C has coordinates (4, 3)

To find: coordinates of point D

The midpoint of line AB conatining points $(x_1, y_1)$ and $(x_2, y_2)$ is given as:

$\text {midpoint}(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here in this problem,

Midpoint (C, D) = (2, 5)

$point C (x_1, y_1) = (4, 3)$

$\text {point } D\left(x_{2}, y_{2}\right)=?$

Subsituting the values in formula we get,

$(2,5)=\left(\frac{4+x_{2}}{2}, \frac{3+y_{2}}{2}\right)$

On comparing both the sides we get,

$2=\frac{4+x_{2}}{2} \text { and } 5=\frac{3+y_{2}}{2}$

$\begin{array}{l}{4=4+x_{2} \text { and } 10=3+y_{2}} \\\\ {\text {Therefore } x_{2}=0 \text { and } y_{2}=7}\end{array}$

Thus the coordinates of point D is (0, 7)