Question

write the coordinates of the vertices after a translation 5 units left and 10 units down.

Explanation:

Step1: Recall translation rule

For a translation $a$ units left and $b$ units down, the rule for a point $(x,y)$ is $(x - a,y - b)$. Here $a = 5$ and $b=10$.

Step2: Find coordinates of point S

The original coordinates of point S are $(1,0)$. Using the translation rule, the new $x$-coordinate is $1-5=-4$ and the new $y$-coordinate is $0 - 10=-10$. So $S'(-4,-10)$.

Step3: Find coordinates of point T

The original coordinates of point T are $(1,7)$. The new $x$-coordinate is $1-5=-4$ and the new $y$-coordinate is $7 - 10=-3$. So $T'(-4,-3)$.

Step4: Find coordinates of point U

The original coordinates of point U are $(8,7)$. The new $x$-coordinate is $8-5 = 3$ and the new $y$-coordinate is $7-10=-3$. So $U'(3,-3)$.

Step5: Find coordinates of point V

The original coordinates of point V are $(8,0)$. The new $x$-coordinate is $8-5 = 3$ and the new $y$-coordinate is $0-10=-10$. So $V'(3,-10)$.

Answer:

$S'(-4,-10)$
$T'(-4,-3)$
$U'(3,-3)$
$V'(3,-10)$