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 the point \( C \) from its reflection point \( C' \) across the x-axis, we can use the properties of reflections. The coordinates of a point \( C' \) that is the reflection of a point \( C \) across the x-axis can be obtained by changing the sign of the y-coordinate of \( C \).

Given that the coordinates of the reflection point \( C' \) are \( (2, -2) \), we know:

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

Thus, the coordinates of point \( C \) are \( (2, 2) \).