Question

behind the figure below is rotated 180° counterclockwise in the translate Left 4 units what are the coordinates of the image of Point C after the transformations

Answer 1

In transformations, the Pre-Image is the original figure and the Image is the figure obtained after the transformation.

You need to identify that coordinates of the point C. Analyzing the graph, you can see that:

`C(4,-9)`

By definition, the rule for a Rotation of 180 degrees counterclockwise centered at the Origin, is:

`\mleft(x,y\mright)\to(-x,-y)`

Knowing that the figure is also translated left 4 units, you must subtract 4 units from the x-coordinate of the point after the Rotation.

Based on the above, you can determine that the coordinates of the point C' (the Image of the point C) is:

`C(4,-9)\rightarrow C^(\prime)((-4-4),9)\rightarrow C^(\prime)(-8,9)`

The answer is:

`C^(\prime)(-8,9)`