Question

give the coordinates of the new image.

1. quadrilateral stuv with vertices s(-3, -3), t(3, -5), u(6, -7), and v(-2, -7): y = -4

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ over the horizontal line $y = k$, the $x$-coordinate remains the same, and the new $y$-coordinate is $2k - y$. Here $k=-4$.

Step2: Find new coordinates for point S

For $S(-3,-3)$, $x=-3$ remains the same. The new $y$-coordinate is $2\times(-4)-(-3)=-8 + 3=-5$. So $S'(-3,-5)$.

Step3: Find new coordinates for point T

For $T(3,-5)$, $x = 3$ remains the same. The new $y$-coordinate is $2\times(-4)-(-5)=-8 + 5=-3$. So $T'(3,-3)$.

Step4: Find new coordinates for point U

For $U(6,-7)$, $x = 6$ remains the same. The new $y$-coordinate is $2\times(-4)-(-7)=-8 + 7=-1$. So $U'(6,-1)$.

Step5: Find new coordinates for point V

For $V(-2,-7)$, $x=-2$ remains the same. The new $y$-coordinate is $2\times(-4)-(-7)=-8 + 7=-1$. So $V'(-2,-1)$.

Answer:

$S'(-3,-5)$
$T'(3,-3)$
$U'(6,-1)$
$V'(-2,-1)$