In the standard (x, y) coordinate plane, a line segment has endpoints at (3, -4) and (9, 8… — ACT

In the standard $(x, y)$ coordinate plane, a line segment has endpoints at $(3, -4)$ and $(9, 8)$ . What is the $y$ -coordinate of the midpoint of this line segment?

Answer: 2

Answer

The

y

-coordinate of the midpoint is

2

The

y

-coordinate of the midpoint is calculated by finding the average of the

y

-coordinates of the endpoints:

\frac{y_1 + y_2}{2}

. Substituting

y_1 = -4

and

y_2 = 8

gives

\frac{-4 + 8}{2} = \frac{4}{2} = 2

Step-by-Step Solution

Identify the

y

-coordinates of the two given endpoints

(3, -4)

and

(9, 8)

y_1 = -4

and

y_2 = 8

The midpoint formula relies on the coordinates of the endpoints.

Calculate the average of the

y

-coordinates using the formula

y_m = \frac{y_1 + y_2}{2}

y_m = \frac{-4 + 8}{2} = 2

The

y

-coordinate of a midpoint is the arithmetic mean of the

y

-coordinates of the endpoints.

Key Concept

Midpoint Formula

Estimated Time:45s

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