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?

Answer 1

To find the coordinates of point C, we need to understand how reflections across the x-axis work. When a point (x, y) is reflected across the x-axis, its y-coordinate changes sign, while the x-coordinate remains the same.

Given that the reflection point C′ has coordinates (2, −2), we can deduce the coordinates of the original point C by changing the sign of the y-coordinate of C′.

Starting with the coordinates of C′:
- \( C' = (2, -2) \)

The reflection across the x-axis means the corresponding point C will have the same x-coordinate and the opposite y-coordinate:
- The x-coordinate of C is the same as that of C′, which is 2.
- The y-coordinate of C is the opposite of the y-coordinate of C′, which is \( -(-2) = 2 \).

Therefore, the coordinates of point C are:
- \( C = (2, 2) \)

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