Question

What are the coordinates of R' for the dilation D(0.5. p)(PQRS)?

Answer 1

Answer:

$R' = (-1,-0.5)$

Step-by-step explanation:

See attachment for complete question.

From the attachment:

$P = (-3,-3)$

$R = (1,2)$

Dilation:

$D_{(0.5,P)}$

Required

Determine R'

First, subtract the coordinates of P from R. This means that R is measured from P.

$R = (1-(-3),2-(-3))$

$R = (1+3,2+3)$

$R = (4,5)$

Next, apply dilation factor 0.5

$R' = R * 0.5$

$R' = (4,5) * 0.5$

$R' = (4* 0.5,5* 0.5)$

$R' = (2,2.5)$

Lastly, measure R' from the origin by adding the coordinates of P to R'

$R' = (2+(-3),2.5+(-3))$

$R' = (2-3,2.5-3)$

$R' = (-1,-0.5)$

Answer 2

Dilation of a figure or image is to enlarge or shorter it from the original length by a scale factor.

The coordinate of the R' after the dilation is (-1,-0.5)

What is dilation?

Dilation of a figure or image is to enlarge or shorter it from the original length by a scale factor.

Given information-

The points of PQRS are Q(-3,2), R(1,2), P(-3,-3), S(1,-3).

The given points are dilated. This dilation can be measured by subtracting the point P from each point . Thus the point of Q is,

$Q'=Q-P\\Q'=(-3-(-3), 2-(-3))\\Q'=(0,5)$

Similarly,

$R'=R-P= (1-(-3),2-(-3))=(4,5)\\P'=P-P=(-3-(-3), 3-(-3)=(0,0)\\S'=S-P=(1-(-3),-3-(-3))=(4,0)$

As the dilation factor is 0.5. Thus, the point of Q is,

$Q"=(0.5)\times(0,5)=(0,2.5)$

Similarly,

$R"=(0.5)\times(4,5)=(2,2.5)\\P"=(0.5)\times(0,0)=(0,0)\\S"=(0.5)\times(4,0)=(2,0)$

Add the points P back, to the above coordinate plane to get the dilation point. Thus the point of Q is,

$Q'''=(0,+(-3), 2.5+(-3))\\Q'''=(-3,-0.5)$

Similarly,

$R'''=(2+(-3),2.5+(-3))=(-1,-0.5)\\P'''=(0+(-3),0+(-3))=(-3,-3)\\S'''=(2+(-3),0+(-3))=(-1,-3)$

Thus the coordinate of the R' after the dilation is (-1,-0.5)

Learn more about the dilation here;

https://brainly.com/question/10253650