Question

graph the image of rectangle tuvw after a reflection over the line x = 2.

Explanation:

Step1: Recall reflection rule

For a reflection over the line $x = a$, the formula for reflecting a point $(x,y)$ is $(2a - x,y)$. Here $a = 2$.

Step2: Identify rectangle vertices

Assume the coordinates of the vertices of rectangle $TUVW$ are $T(-6,-5)$, $U(-2,-5)$, $V(-2,3)$, $W(-6,3)$.

Step3: Apply reflection formula to point T

For $T(-6,-5)$, using the formula $(2a - x,y)$ with $a = 2$, we get $(2\times2-(-6),-5)=(4 + 6,-5)=(10,-5)$.

Step4: Apply reflection formula to point U

For $U(-2,-5)$, we have $(2\times2-(-2),-5)=(4 + 2,-5)=(6,-5)$.

Step5: Apply reflection formula to point V

For $V(-2,3)$, we get $(2\times2-(-2),3)=(4 + 2,3)=(6,3)$.

Step6: Apply reflection formula to point W

For $W(-6,3)$, we have $(2\times2-(-6),3)=(4 + 6,3)=(10,3)$.

Step7: Graph new rectangle

Plot the points $(10,-5)$, $(6,-5)$, $(6,3)$, $(10,3)$ and connect them to form the reflected rectangle.

Answer:

Graph the rectangle with vertices $(10,-5)$, $(6,-5)$, $(6,3)$, $(10,3)$ on the given coordinate - grid.