Question

J is the midpoint of HK, H has coordinates (5,-3), and J has coordinates (7,3). Find the coordinates of K.The coordinates of K are

Answer 1

Answer:

The coordinates of K is;

$(9,9)$

Explanation:

We want to find the coordinates of point K.

Given that J is the midpoint of HK and;

H has coordinates (5,-3)

J has coordinates (7,3).

The formula for calculating midpoint is;

$\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}$

where x1 and x2 are the x coordinates of the endpoints and y1 and y2 are the y coordinates of the endpoints.

To get the coordinates of one of the endpoints, we have;

$\begin{gathered} x_2=2x-x_1 \\ y_2=2y-y_1 \end{gathered}$

substituting the given coordinates of the mid point and endpoint;

$\begin{gathered} x_2=2(7)-5 \\ x_2=14-5 \\ x_2=9 \end{gathered}$$\begin{gathered} y_2=2(3)-(-3) \\ y_2=6+3 \\ y_2=9 \end{gathered}$

Therefore, the coordinates of K is;

$(9,9)$