Question

A = (5, 1)
B = (3.5, 3.5)

Andrea has to find a third point, C, to form a triangle on the coordinate plane shown. She is told the coordinates of its reflection point, C′, across the x-axis are (2,−2). What are the coordinates of point C?

Answer 1

To find the coordinates of point \( C \) given its reflection point \( C' \) across the x-axis, we remember that when a point \( (x, y) \) is reflected across the x-axis, the resulting point is \( (x, -y) \).

Given that \( C' = (2, -2) \), we can find the coordinates of point \( C \) by reflecting \( C' \) back across the x-axis.

1. The x-coordinate of \( C \) remains the same as that of \( C' \): \( x = 2 \).
2. The y-coordinate of \( C \) is the opposite of that of \( C' \): \( y = -(-2) = 2 \).

Thus, the coordinates of point \( C \) are:

\[
C = (2, 2)
\]

So, the coordinates of point \( C \) are \( \boxed{(2, 2)} \).