Andrea has to find a third point, C

Question

, 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 can use the following principle: When a point \( (x, y) \) is reflected across the x-axis, the new coordinates become \( (x, -y) \).

Given the coordinates of the reflection point \( C' = (2, -2) \), we denote the coordinates of point \( C \) as \( (x, y) \).

Since \( C' \) is the reflection of \( C \) across the x-axis, we have: \[ C' = (x, -y) \]

Given that \( C' = (2, -2) \), we can equate the coordinates:

1. \( x = 2 \)
2. \( -y = -2 \) which implies \( y = 2 \)

Thus, the coordinates of point \( C \) are: \[ C = (2, 2) \]

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