In the standard (x,y) coordinate plane, the midpoint of a line segment is (2, 5). If one o… — ACT

In the standard $(x,y)$ coordinate plane, the midpoint of a line segment is $(2, 5)$ . If one of the endpoints of the segment is $(-2, 1)$ , what is the $x$ -coordinate of the other endpoint?

Answer: 6

Answer

The

x

-coordinate of the other endpoint is 6.

According to the midpoint formula, the

x

-coordinate of the midpoint is the average of the

x

-coordinates of the two endpoints. Substituting the given values yields the equation

2 = \frac{-2 + x_2}{2}

. Multiplying both sides by 2 gives

4 = -2 + x_2

, and adding 2 to both sides results in

x_2 = 6

Step-by-Step Solution

Set up the midpoint equation for the

x

-coordinate using the midpoint formula

x_m = \frac{x_1 + x_2}{2}

2 = \frac{-2 + x_2}{2}

The

x

-coordinate of the midpoint is the average of the

x

-coordinates of the endpoints.

Multiply both sides of the equation by 2 to solve for the numerator.

4 = -2 + x_2

Multiplying by 2 eliminates the denominator on the right side.

Add 2 to both sides of the equation to isolate

x_2

x_2 = 6

Adding 2 to both sides isolates the variable

x_2

Key Concept

Midpoint Formula

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