Question

reflect the figure over the line y = x + 4. plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

Step1: Recall reflection formula

The formula to reflect a point $(x_0,y_0)$ over the line $y = x + c$ is obtained by first translating the line to the origin (subtract $c$ from $y$ - axis), reflect over $y=x$ and then translate back. The general formula for reflecting a point $(x_0,y_0)$ over $y=x + c$ is $(y_0 - c,x_0 + c)$.

Step2: Identify vertices of the polygon

Let's assume the vertices of the polygon in the given figure are $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$. For each vertex, apply the reflection formula $y=x + 4$. So the new vertices will be $(y_1-4,x_1 + 4),(y_2-4,x_2 + 4),(y_3-4,x_3 + 4),(y_4-4,x_4 + 4)$.

Step3: Plot the reflected points

Plot the new - obtained points on the coordinate plane and connect them in the same order as the original polygon to get the reflected figure.

Since we don't have the exact coordinates of the vertices from the image, we can't give the numerical answer for the reflected points. But the general process for reflection over the line $y=x + 4$ is as described above.

Answer:

Step1: Recall reflection formula

The formula to reflect a point $(x_0,y_0)$ over the line $y = x + c$ is obtained by first translating the line to the origin (subtract $c$ from $y$ - axis), reflect over $y=x$ and then translate back. The general formula for reflecting a point $(x_0,y_0)$ over $y=x + c$ is $(y_0 - c,x_0 + c)$.

Step2: Identify vertices of the polygon

Let's assume the vertices of the polygon in the given figure are $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$. For each vertex, apply the reflection formula $y=x + 4$. So the new vertices will be $(y_1-4,x_1 + 4),(y_2-4,x_2 + 4),(y_3-4,x_3 + 4),(y_4-4,x_4 + 4)$.

Step3: Plot the reflected points

Plot the new - obtained points on the coordinate plane and connect them in the same order as the original polygon to get the reflected figure.

Since we don't have the exact coordinates of the vertices from the image, we can't give the numerical answer for the reflected points. But the general process for reflection over the line $y=x + 4$ is as described above.