Andrea has to find a third point, C

Question

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

(1 point)

Answer 1

To find the coordinates of point \( C \) given its reflection point \( C' \) across the x-axis, we can use the property of reflections. When a point \( (x, y) \) is reflected across the x-axis, the new coordinates become \( (x, -y) \).

Given that the coordinates of \( C' \) are \( (2, -2) \), we can set up the equations based on the reflection properties:

1. The x-coordinate of point \( C \) will remain the same as that of \( C' \), which is 2.
2. The y-coordinate of point \( C \) will be the negative of the y-coordinate of \( C' \). Since \( C' \) has a y-coordinate of -2, the y-coordinate of \( C \) will be \( -(-2) = 2 \).

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