Question

Question content area top Part 1 Find the midpoint of the line segment joining points A and B. A(8,-5) B(2,1) ​;

Answer 1

`(5,\, -2)`.

Explanation:

For a line segment in a plane, the
`x`-coordinates of the midpoint is the average of the
`x\!`-coordinates of the endpoints. Likewise, the
`y`-coordinates of the midpoint is the average of the
`y\!` coordinates of the endpoints.

For example, the midpoint of the line segment joining
`(x_(a),\, y_(a))` and
`(x_(b),\, y_(b))` is:

`\begin{aligned} \left((x_(a) + x_(b))/(2),\, (y_(a) + y_(b))/(2)\right)\end{aligned}`.

In this question,
`x_(a) = 8`,
`x_(b) = 2`,
`y_(a) = (-5)`,
`y_(b) = 1`. Thus, the midpoint of the line segment joining the two points would be:

`\begin{aligned} \left((8 + 2)/(2),\, ((-5) + 1)/(2)\right)\end{aligned}`.

Simplify to obtain:

`\begin{aligned} \left(5,\, -2\right)\end{aligned}`.

Hence, the midpoint of the line segment joining
`(8,\, -5)` and
`(2,\, 1)` would be
`(5,\, -2)`.