Question

What is the midpoint of line segment QP given Q(6, 3) and P(-6, -1).

Answer 1

`\begin{gathered} \text{Given} \\ Q(6,3) \\ P(-6,-1) \end{gathered}`

Recall that given two points, the midpoint of a line segment is determined by the formula

`\begin{gathered} M=\mleft((x_1 + x_2)/(2),\; (y_1 + y_2)/(2)\mright) \\ \text{where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the two endpoints of the line segment} \end{gathered}`

Substitute the following and we get

`\begin{gathered} (x_1,y_1)=(6,3) \\ (x_2,y_2)=(-6,-1) \\ \\ M=\mleft((x_1 + x_2)/(2),\; (y_1 + y_2)/(2)\mright) \\ M=\mleft((6 + -6)/(2),\; (3 + -1)/(2)\mright) \\ M=\mleft((0)/(2),\; (2)/(2)\mright) \\ M=(0,\; 1) \end{gathered}`

Therefore, the midpoint of line segment is (0,1)