Question

the figure below is translated right 4 units and then rotated 180° counterclockwise. what are the coordinates of the image of point c after these transformations? (the image shows a coordinate plane with a triangle, and point c is marked. the coordinate plane has x-axis from -12 to 12 and y-axis from -12 to 12.)

Explanation:

Step1: Find original coordinates of C

From the graph, point C has coordinates \((-8, -7)\).

Step2: Apply translation right 4 units

To translate a point \((x, y)\) right 4 units, we add 4 to the x - coordinate. So the new coordinates after translation are \((-8 + 4, -7)=(-4, -7)\).

Step3: Apply 180° counterclockwise rotation

The rule for a 180° counterclockwise (or clockwise) rotation about the origin is \((x, y)\to(-x, -y)\). Applying this to the point \((-4, -7)\), we get \((-(-4), -(-7))=(4, 7)\).

Answer:

\((4, 7)\)