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Question

A coordinate plane shows the x and y axes ranging from negative 6 to 6 in increments of 1. A line joins two plotted points, upper A and upper B. The coordinates of the plotted points are as follows: upper A is left parenthesis 5 comma 1 right parenthesis and upper B is left parenthesis 3.5 comma 3.5 right parenthesis.

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
?

(1 point)

Answer 1

To find the coordinates of point \( C \) given its reflection across the x-axis, we start from the coordinates of its reflection point \( C' \), which is \( (2, -2) \).

The rule for reflecting a point across the x-axis is that the x-coordinate remains the same while the y-coordinate changes sign. Therefore, if \( C' \) is \( (2, -2) \), then the coordinates of point \( C \) will have the same x-coordinate but the opposite sign for the y-coordinate.

Thus, the coordinates of point \( C \) can be calculated as follows:

\[ C = (x, -y) = (2, -(-2)) = (2, 2) \]

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