5.) The vertices of a triangle are P(4, 1), Q(2, -8), and R(-8, 1). What are the vertices of the image reflected across the y-axis?
a.) P'(4, -1), Q'(2, 8), and R'(-8, -1)
b.) P'(-4, 1), Q'(-2, -8), and R'(8, -1)
c.) P'(4, -1), Q'(-2, 8), and R'(8, -1)
d.) P'(4, 1), Q'(2, 8), and R'(-8, 1)
The vertices of the image reflected across the y-axis will have the same x-coordinate as the original vertices but the y-coordinate will change sign.
So the correct answer is:
c.) P'(4, -1), Q'(-2, 8), and R'(8, -1)
To find the image of a point reflected across the y-axis, you need to change the sign of the x-coordinate while keeping the y-coordinate the same.
Given the vertices of the triangle: P(4, 1), Q(2, -8), R(-8, 1)
Let's find the reflected points:
The image of P(4, 1) would be P'(-4, 1) since we change the sign of the x-coordinate.
The image of Q(2, -8) would be Q'(-2, -8) since we change the sign of the x-coordinate.
The image of R(-8, 1) would be R'(8, 1) since we change the sign of the x-coordinate.
So, the vertices of the image reflected across the y-axis are P'(-4, 1), Q'(-2, -8), and R'(8, 1).
Therefore, the correct answer is option (b): P'(-4, 1), Q'(-2, -8), and R'(8, -1).
To reflect a point across the y-axis, we simply change the sign of its x-coordinate while keeping the y-coordinate unchanged.
Given the vertices of the triangle are P(4, 1), Q(2, -8), and R(-8, 1), let's apply the reflection across the y-axis to each point:
Reflecting P(4, 1):
- Change the sign of the x-coordinate: (-4, 1)
The vertex P' is (-4, 1).
Reflecting Q(2, -8):
- Change the sign of the x-coordinate: (-2, -8)
The vertex Q' is (-2, -8).
Reflecting R(-8, 1):
- Change the sign of the x-coordinate: (8, 1)
The vertex R' is (8, 1).
Therefore, the vertices of the triangle after reflecting across the y-axis are P'(-4, 1), Q'(-2, -8), and R'(8, 1).
The correct answer is b.) P'(-4, 1), Q'(-2, -8), and R'(8, -1).