Question

21. Find the y-coordinate of point M, the midpoint of AB, for A(-3, 3) and B(5, 7).

(Lesson 1-4)
A. -1
B. 1
C. 2
D. 5

Answer 1

The
`y`-coordinate of this midpoint is
`5`.

Explanation:

Let
`{\sf A}` and
`{\sf B}` denote two points in the cartesian plane.

If point
`{\sf A}` is at
`(x_(a),\, y_(a))` while point
`{\sf B}` is at
`(x_(b),\, y_(b))`, the midpoint of
`{\sf AB}` would be at:

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

In other words, the
`y`-coordinate of the midpoint of
`{\sf AB}` would be the average of the
`y\!`-coordinates of point
`{\sf A}` and point
`{\sf B}`.

In this question, the
`y`-coordinates of point
`{\sf A}` and point
`{\sf B}` are
`3` and
`7`, respectively. The
`y\!`-coordinate of the midpoint of
`{\sf A}\!` and
`{\sf B}` would be the mean
`(3 + 7) / (2) = 5`.