Question

the figure below is rotated 180° counterclockwise and then translated left 2 units. what are the coordinates of the image of point y after these transformations?

Explanation:

1. First, assume the original coordinates of point \(Y\) are \((x,y)\). From the graph, we can see that the original coordinates of point \(Y\) are \((- 3,-9)\).

• Rule for \(180^{\circ}\) counter - clockwise rotation:
• The rule for rotating a point \((x,y)\) \(180^{\circ}\) counter - clockwise about the origin is \((x,y)\to(-x,-y)\).
• For the point \(Y(-3,-9)\), after a \(180^{\circ}\) counter - clockwise rotation, the new coordinates \(Y_1\) are \((-(-3),-(-9))=(3,9)\).
• Rule for translation:
• The rule for translating a point \((x,y)\) left \(2\) units is \((x,y)\to(x - 2,y)\).
• For the point \(Y_1(3,9)\), after translating left \(2\) units, the new coordinates \(Y_2\) are \((3 - 2,9)=(1,9)\).

Answer:

\((1,9)\)