Question

Rectangle CDEF has vertices C(−10, 10), D(5, 10), E(5, 5), and F(−10, 5). It is dilated by a scale factor of 15 centered at (0, 0) to produce rectangle C′D′E′F′. What is the perimeter in units of rectangle C′D′E′F′?

How many units are there?

Answer 1

Answer:

tzxtfdtdttdtfzffzfzff

Answer 2

Answer:

DILATION

Step-by-step explanation:

From the graph, we can see that

• $CD=15$ units
• $DE=5$ units
• $EF=15$ units
• $FC=5$ units

A dilation changes the distance between points by multiplying the x and y coordinates by the scale factor.

After the dilation by a scale factor of $15$ units centered at $(0,0)$, we get that

$C'D'=15CD\\C'D'=(15)^2\\C'D'=225$units

$D'E'=15DE\\D'E'=15(5)\\D'E'=75$units

$E'F'=15EF\\E'F'=(15)^2\\E'F'=225$units

$F'C'=15FC\\F'C'=15(5)\\F'C'=75$units

Therefore, the perimeter in units of rectangle $C'D'E'F'$ is $=225+75+225+75=600$ units.

So, the perimeter of the rectangle $C'D'E'F'$ after the dilation is $600$ units.