Question

7 graph the image of the figure. translation: 4 units right and 5 units down polygon

Explanation:

Step1: Recall translation rule

For a point $(x,y)$ translated 4 units right and 5 units down, the new - point is $(x + 4,y-5)$.

Step2: Identify original points

Assume the vertices of the polygon are $A(x_1,y_1)$, $B(x_2,y_2)$ and $C(x_3,y_3)$. From the graph, if we assume $A(- 2,3)$, $B(1,2)$ and $C(0,4)$.

Step3: Calculate new points

For point $A$: $x_1=-2,y_1 = 3$, new point $A'$ has coordinates $(-2 + 4,3-5)=(2,-2)$.
For point $B$: $x_2 = 1,y_2=2$, new point $B'$ has coordinates $(1 + 4,2-5)=(5,-3)$.
For point $C$: $x_3=0,y_3 = 4$, new point $C'$ has coordinates $(0 + 4,4-5)=(4,-1)$.

Step4: Graph new polygon

Plot the points $A'(2,-2)$, $B'(5,-3)$ and $C'(4,-1)$ on the coordinate - plane and connect them to form the translated polygon.

Since we can't actually graph in this text - based format, the key is to find the new coordinates of the vertices of the polygon. The new coordinates of the vertices of the translated polygon are found as above.

Answer:

Step1: Recall translation rule

For a point $(x,y)$ translated 4 units right and 5 units down, the new - point is $(x + 4,y-5)$.

Step2: Identify original points

Assume the vertices of the polygon are $A(x_1,y_1)$, $B(x_2,y_2)$ and $C(x_3,y_3)$. From the graph, if we assume $A(- 2,3)$, $B(1,2)$ and $C(0,4)$.

Step3: Calculate new points

For point $A$: $x_1=-2,y_1 = 3$, new point $A'$ has coordinates $(-2 + 4,3-5)=(2,-2)$.
For point $B$: $x_2 = 1,y_2=2$, new point $B'$ has coordinates $(1 + 4,2-5)=(5,-3)$.
For point $C$: $x_3=0,y_3 = 4$, new point $C'$ has coordinates $(0 + 4,4-5)=(4,-1)$.

Step4: Graph new polygon

Plot the points $A'(2,-2)$, $B'(5,-3)$ and $C'(4,-1)$ on the coordinate - plane and connect them to form the translated polygon.

Since we can't actually graph in this text - based format, the key is to find the new coordinates of the vertices of the polygon. The new coordinates of the vertices of the translated polygon are found as above.