In the standard (x, y) coordinate plane, line segment CD has endpoints C(-2, 2) and D(-2, … — ACT

In the standard $(x, y)$ coordinate plane, line segment $CD$ has endpoints $C(-2, 2)$ and $D(-2, 8)$ . If segment $CD$ is reflected across the $y$ -axis to form segment $C'D'$ , what are the coordinates of the midpoint of segment $C'D'$ ?

$(2, 5)$ Answer
B
$(-2, 5)$
C
$(-2, -5)$
D
$(2, -5)$
E
$(5, 2)$

Answer

The coordinate point

(2, 5)

The correct answer is

(2, 5)

because the midpoint of the original segment

CD

is located at

(-2, 5)

. When a point is reflected across the

y

-axis, its

x

-coordinate changes sign while its

y

-coordinate remains the same. Therefore, the image of the midpoint is

(2, 5)

Step-by-Step Solution

Find the midpoint of the original segment

CD

Midpoint

M = \left(\frac{-2 + (-2)}{2}, \frac{2 + 8}{2}\right) = (-2, 5)

The midpoint formula is

M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)

Apply the reflection across the

y

-axis to the midpoint.

M' = (-(-2), 5) = (2, 5)

Reflecting a point

(x, y)

across the

y

-axis maps it to

(-x, y)

Key Concept

Reflection of points and segments across the axes in the coordinate plane

Alternative Method

Instead of finding the midpoint first, you can reflect the endpoints

C(-2, 2)

and

D(-2, 8)

across the

y

-axis to get

C'(2, 2)

and

D'(2, 8)

. Then, apply the midpoint formula to these new coordinates to get the midpoint:

\left(\frac{2 + 2}{2}, \frac{2 + 8}{2}\right) = (2, 5)

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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