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.

Question

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

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Answer 1

To find the coordinates of point \( C \) given its reflection point \( C' \) across the x-axis, we need to recall how reflections across the x-axis work.

When a point \( (x, y) \) is reflected across the x-axis, the x-coordinate remains the same while the y-coordinate changes sign. Thus, if the reflection point \( C' \) has coordinates \( (2, -2) \), then the original point \( C \) must have the same x-coordinate and the opposite sign for the y-coordinate.

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

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

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

\[ C(2, 2) \]

So the answer is \( (2, 2) \).