Question

write the coordinates of the vertices after a translation 4 units right and 1 unit down.

Explanation:

Step1: Identify original coordinates

Assume $P(1,-2)$, $Q(1,5)$, $R(-9,-3)$

Step2: Apply translation rule for x - coordinate

For a translation 4 units right, add 4 to the x - coordinate of each point.
$P_x'=1 + 4=5$, $Q_x'=1 + 4=5$, $R_x'=-9 + 4=-5$

Step3: Apply translation rule for y - coordinate

For a translation 1 unit down, subtract 1 from the y - coordinate of each point.
$P_y'=-2-1=-3$, $Q_y'=5 - 1=4$, $R_y'=-3-1=-4$

Step4: Write new coordinates

The new coordinates are $P'(5,-3)$, $Q'(5,4)$, $R'(-5,-4)$

Answer:

$P'(5,-3)$, $Q'(5,4)$, $R'(-5,-4)$