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:

Step1: Determine original coordinates

Assume the coordinates of point Y are \((x,y)\). From the graph, if we estimate, assume \(Y(-8, - 4)\).

Step2: Apply 180 - degree counter - clockwise rotation rule

The rule for a 180 - degree counter - clockwise rotation about the origin \((0,0)\) is \((x,y)\to(-x,-y)\). For point \(Y(-8,-4)\), after rotation, the coordinates become \((8,4)\).

Step3: Apply left - translation rule

The rule for translating a point left by 2 units is \((x,y)\to(x - 2,y)\). For the point \((8,4)\) after rotation, after translation left 2 units, the new coordinates are \((8-2,4)=(6,4)\).

Answer:

\((6,4)\)