Exercise 5 Page 472

We know that point D is translated 5 units right and 2 units down. Then, it is reflected over the y-axis. We want to find the coordinates of point D after both transformations. We will perform one transformation at a time. Let's consider the given point and mark its coordinates.

When a figure is translated, the x-coordinate of the preimage changes by the value of the horizontal translation a. The y-coordinate of the preimage changes by the vertical translation b. (x,y) → (x + a, y + b)We want to perform a translation by 5 units right and 2 units down. The formula represents a translation a units right and b units up. Therefore we will substitute - 2 for b. (x,y) → (x + 5, y +( - 2)) We know that the preimage is at point (- 4,2). Therefore, we can substitute - 4 for x and 2 for y.

We found that the point D(- 4,2) after a translation 5 units right and 2 units down is located at D'(1,0).

Now we will apply a reflection over the y-axis. To reflect a figure over the y-axis, we multiply the x-coordinates by - 1.

We found that the coordinates of point D after a translation 5 units right and 2 units down and a reflection over the y-axis are (- 1,0). This corresponds to option C.