Question

write the coordinates of the vertices after a dilation with a scale factor of 5 about the origin.

Explanation:

Step1: Recall dilation formula

For a dilation about the origin with scale - factor $k$, if a point has coordinates $(x,y)$, the new coordinates $(x',y')$ after dilation are given by $(x',y')=(k\cdot x,k\cdot y)$. Here $k = 5$.

Step2: Find coordinates of point B

The coordinates of point B are $(-2,-2)$. Using the dilation formula, $x'=5\times(-2)=-10$ and $y'=5\times(-2)=-10$. So the new coordinates of B are $(-10,-10)$.

Step3: Find coordinates of point C

The coordinates of point C are $(-2,0)$. Using the dilation formula, $x'=5\times(-2)=-10$ and $y'=5\times0 = 0$. So the new coordinates of C are $(-10,0)$.

Step4: Find coordinates of point D

The coordinates of point D are $(2,0)$. Using the dilation formula, $x'=5\times2 = 10$ and $y'=5\times0=0$. So the new coordinates of D are $(10,0)$.

Step5: Find coordinates of point E

The coordinates of point E are $(2,-2)$. Using the dilation formula, $x'=5\times2 = 10$ and $y'=5\times(-2)=-10$. So the new coordinates of E are $(10,-10)$.

Answer:

B$(-10,-10)$, C$(-10,0)$, D$(10,0)$, E$(10,-10)$