Reflections Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
2 of 52 of 5 Items

Question
Use the image to answer the question.

A vertical line separates 2 triangles. The triangle to the left of the line is made up of points upper A, upper B, and upper C, while the triangle on the right is made up of points upper A prime, upper B prime, and upper C prime.

Triangle ABC
has been reflected over a vertical line of reflection. The coordinates of vertices A
, B
, C
, and B′
are shown. What are the coordinates of vertex A′
?

(1 point)
The coordinates of vertex A′
are (
,
).

Answer 1

To determine the coordinates of vertex \( A' \) after reflecting triangle \( ABC \) over a vertical line, we need to know the coordinates of vertex \( A \) and the line of reflection.

Assuming the coordinates of vertex \( A \) are \( (x_A, y_A) \) and the vertical line of reflection is at \( x = k \), then the reflection of \( A \) would be at the point \( A' \).

The formula for finding the reflected coordinates \( A' \) based on the line of reflection is:

• The x-coordinate of the reflected point is given by: \( x' = k - (x_A - k) = 2k - x_A \)

• The y-coordinate remains the same, hence: \( y' = y_A \)

Without loss of generality, please provide the coordinates of vertex \( A \) and the line of reflection so that I can assist you in finding the exact coordinates for \( A' \).