Questions: The figure below is reflected over x-axis and then translated right 5 units. What are the coordinates of the image of point Q after these transformations?

The figure below is reflected over x-axis and then translated right 5 units. What are the coordinates of the image of point Q after these transformations?

Transcript text: The figure below is reflected over $x$-axis and then translated right 5 units. What are the coordinates of the image of point Q after these transformations?

Solution

Solution Steps

Step 1: Identify the coordinates of point Q

Point Q is located at (-2, 2) on the graph.

Step 2: Reflect point Q over the x-axis

Reflecting point Q over the x-axis changes its y-coordinate to the negative of its original value. Therefore, the coordinates of the reflected point Q' are (-2, -2).

Step 3: Translate point Q' right 5 units

Translating point Q' right 5 units increases its x-coordinate by 5. Therefore, the coordinates of the translated point Q'' are (-2 + 5, -2), which simplifies to (3, -2).