Question

graph the image of the figure using the transformation given. 9) reflection across y = 2

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected across the horizontal line $y = k$, the new - point $(x,y')$ is given by the formula $y'=2k - y$. Here $k = 2$.

Step2: Identify vertices of triangle

Let's assume the vertices of triangle $STU$ are $S(x_1,y_1)$, $T(x_2,y_2)$, and $U(x_3,y_3)$.

Step3: Apply reflection formula to each vertex

For vertex $S(x_1,y_1)$, the new $y$ - coordinate $y_1'=2\times2 - y_1=4 - y_1$, and the $x$ - coordinate remains $x_1$. So the new vertex is $S'(x_1,4 - y_1)$.
For vertex $T(x_2,y_2)$, the new $y$ - coordinate $y_2'=2\times2 - y_2=4 - y_2$, and the $x$ - coordinate remains $x_2$. So the new vertex is $T'(x_2,4 - y_2)$.
For vertex $U(x_3,y_3)$, the new $y$ - coordinate $y_3'=2\times2 - y_3=4 - y_3$, and the $x$ - coordinate remains $x_3$. So the new vertex is $U'(x_3,4 - y_3)$.

Step4: Plot the new triangle

Plot the points $S'$, $T'$, and $U'$ on the coordinate - grid and connect them to form the reflected triangle.

Answer:

Graph the triangle with vertices obtained by applying the formula $(x,4 - y)$ to each vertex of the original triangle $STU$.