Question

Rectangle QRST has coordinates Q ( − 3 , 7 ) , R ( − 3 , 11 ) , S ( 4 , 11 ) , and T ( 4 , 7 ) . Dilate the rectangle by a scale factor of 3 with a center of dilation at the origin. What are the coordinates of rectangle Q 'R 'S 'T '? Explain your reasoning. Q ' ( , ) R ' ( , ) S ' ( , ) T ' ( , ) Is the dilation a reduction or an enlargement? Explain your reasoning.​

can someone also give me the rest of the answers for Rising, Running, Stepping, Scaling Part 2 Quiz

Answer 1

Answer: Q'(-9,21), R'(-9,33), S'(12,33) and T'(12,21)

It is enlargement.

Explanation:

Given : Rectangle QRST has coordinates Q (− 3 , 7 ) , R (− 3 , 11 ) , S ( 4 , 11 ) , and T ( 4 , 7 ) .

Scale factor =3 >1 , so it is an enlargement. [Figure enlarge using scale factor greater than 1 ]

The rule we use for dilating a figure using center of dilation at the origin and scale factor k:

`(x,y)\to (kx, ky)`

Then, the coordinates of rectangle Q 'R 'S 'T ' will be :-

`Q(-3,7)\to Q'(\ 3(-3)\ ,\ 3(7)\ )=Q'(-9,21)`

`R(-3,11)\to R'(\ 3(-3)\ ,\ 3(11)\ )=R'(-9,33)`

`S(4,11)\to S'(\ 3(4)\ ,\ 3(11)\ )=S'(12,33)`

`T(4,7)\to T'(\ 3(4)\ ,\ 3(7)\ )=T'(12,21)`

Hence, the coordinates of rectangle Q 'R 'S 'T ' are : Q'(-9,21), R'(-9,33), S'(12,33) and T'(12,21)

Answer 2

Because the scale factor is at the origin, you multiply all the coordinates by the scale factor:

Q(-3,7) = Q'(-3*3, 7*3) = Q'(-9,21)

R(-3,11) = R(-3*3, 11*3) = R'(-9,33)

S(4,11) = S'(4*3,11*3) = R'(12,33)

T(4,7) = T'(4*3, 7*3) = T'(12,21)