Question

1. the graph of △pqr is shown. graph the image of △pqr after a reflection across the line y = 4. include the line of reflection. then write the coordinates of the image.

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected across the horizontal line $y = k$, the new - point $(x,y')$ has the formula $y'=2k - y$. Here $k = 4$.

Step2: Assume coordinates of $\triangle PQR$

Let's assume $P(x_1,y_1)$, $Q(x_2,y_2)$, $R(x_3,y_3)$. After reflection across $y = 4$, the new coordinates will be $P'(x_1,8 - y_1)$, $Q'(x_2,8 - y_2)$, $R'(x_3,8 - y_3)$.

Step3: Graph the reflection

To graph the reflection, first draw the line $y = 4$. Then for each vertex of $\triangle PQR$, measure the vertical distance from the vertex to the line $y = 4$. Move the same distance on the opposite side of the line $y = 4$ to get the corresponding vertex of the reflected triangle.

Answer:

The coordinates of the image of $\triangle PQR$ (assuming vertices $P(x_1,y_1)$, $Q(x_2,y_2)$, $R(x_3,y_3)$) are $P'(x_1,8 - y_1)$, $Q'(x_2,8 - y_2)$, $R'(x_3,8 - y_3)$. And the graph should show $\triangle PQR$, the line $y = 4$, and the reflected $\triangle P'Q'R'$.