Question

if (overline{pq}) is reflected across the (y)-axis, what will the endpoints of the reflected line segment be?

options:
((2, 3)) and ((-4, 5))
((2, -3)) and ((4, -5))
((-2, 3)) and ((-4, 5))
((-2, 3)) and ((4, -5))

Explanation:

Step1: Find coordinates of P and Q

From the graph, point \( P \) is at \( (2, 3) \) and point \( Q \) is at \( (4, 5) \).

Step2: Apply reflection over y - axis

The rule for reflecting a point \( (x, y) \) over the \( y \)-axis is \( (x, y)\to(-x, y) \).

For point \( P(2, 3) \):
Using the reflection rule, substitute \( x = 2 \) and \( y=3 \). We get \( (- 2,3) \).

For point \( Q(4, 5) \):
Using the reflection rule, substitute \( x = 4 \) and \( y = 5 \). We get \( (-4,5) \).

Answer:

\( (-2, 3) \) and \( (-4, 5) \) (corresponding to the option: \( (-2, 3) \) and \( (-4, 5) \))