Question

Find the midpoint of the segment with endpoints at (-2,1) and (0,9) using (x1+x2,y1+y2)

Answer 1

(-1, 5)

Explanation:

Midpoint between two points

`\textsf{Midpoint}=\left((x_2+x_1)/(2),(y_2+y_1)/(2)\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)`

Define the endpoints:

• 
  `\textsf{let}\:(x_1,y_1)=(-2,1)`

• 
  `\textsf{let}\:(x_2,y_2)=(0,9)`

Substitute the defined points into the formula:

`\begin{aligned}\implies \textsf{Midpoint} & =\left((x_2+x_1)/(2),(y_2+y_1)/(2)\right)\\\\ & =\left((0+(-2))/(2),(9+1)/(2)\right)\\\\& =\left((-2)/(2),(10)/(2)\right)\\\\& =\left(-1,5\right)\end{aligned}`

Therefore, the midpoint of the segment with endpoints (-2, 1) and (0, 9) is (-1, 5).