Question

reflect the figure over the line y = -5. plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

Step1: Recall reflection rule

For a point $(x,y)$ reflected over the horizontal line $y = k$, the $x$-coordinate remains the same and the new $y$-coordinate is given by $y'=2k - y$. Here $k=-5$.

Step2: Assume a point on the figure

Let's assume a point $(x,y)$ on the original triangle. After reflection over $y = - 5$, the new point is $(x,2\times(-5)-y)=(x,-10 - y)$.

Step3: Apply to all points

For each vertex of the triangle, keep the $x$-value unchanged and calculate the new $y$-value using the formula $y_{new}=-10 - y_{old}$. Then plot these new - formed points to get the reflected figure.

Since no specific points of the original triangle are given in the text (only the instruction and the graph), the general method for reflection over the line $y=-5$ is as above. If we had the coordinates of the vertices of the triangle (say $(x_1,y_1),(x_2,y_2),(x_3,y_3)$), we would calculate the new coordinates as $(x_1,-10 - y_1),(x_2,-10 - y_2),(x_3,-10 - y_3)$ and plot them.

Answer:

Step1: Recall reflection rule

For a point $(x,y)$ reflected over the horizontal line $y = k$, the $x$-coordinate remains the same and the new $y$-coordinate is given by $y'=2k - y$. Here $k=-5$.

Step2: Assume a point on the figure

Let's assume a point $(x,y)$ on the original triangle. After reflection over $y = - 5$, the new point is $(x,2\times(-5)-y)=(x,-10 - y)$.

Step3: Apply to all points

For each vertex of the triangle, keep the $x$-value unchanged and calculate the new $y$-value using the formula $y_{new}=-10 - y_{old}$. Then plot these new - formed points to get the reflected figure.

Since no specific points of the original triangle are given in the text (only the instruction and the graph), the general method for reflection over the line $y=-5$ is as above. If we had the coordinates of the vertices of the triangle (say $(x_1,y_1),(x_2,y_2),(x_3,y_3)$), we would calculate the new coordinates as $(x_1,-10 - y_1),(x_2,-10 - y_2),(x_3,-10 - y_3)$ and plot them.