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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

Sagot :

jacob193

Answer:

The [tex]y[/tex]-coordinate of this midpoint is [tex]5[/tex].

Step-by-step explanation:

Let [tex]{\sf A}[/tex] and [tex]{\sf B}[/tex] denote two points in the cartesian plane.

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

[tex]\begin{aligned}\left(\frac{x_{a} + x_{b}}{2},\, \frac{y_{a} + y_{b}}{2} \right)\end{aligned}[/tex].

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

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

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