Question

The coordinates of the vertices of two rectangles, Rectangle ABCD and Rectangle PQRS are given below.
Rectangle ABCD – A(0, 8), B(8, 8), C(8, -4), D(0, -4)
Rectangle PQRS – P(0, 4), Q(4, 4), R(4, -2), S(0, -2)
Maria scaled both the rectangles about their centers to create two congruent rectangles A′B′C′D′ and P′Q′R′S′.
By which factor did she most likely scale Rectangle ABCD and Rectangle PQRS?

Answer 1

Rectangle ABCD by and Rectangle PQRS by 2 to create congruent rectangles of dimensions 4 x 3 units

Rectangle ABCD by 2 and Rectangle PQRS by 3 to create congruent rectangle of dimensions 3 x 2 units

Rectangle ABCD by and Rectangle PQRS by 4 to create congruent rectangles of dimensions 4 x 3 units

Rectangle ABCD by and Rectangle PQRS by to create congruent rectangles of dimensions 2 x 3 units

Answer 2

@jim_thompson5910

Answer 3

what is the distance from A to B?

Answer 4

8 @jim_thompson5910

Answer 5

what is the distance from P to Q

Answer 6

4

Answer 7

so you want to multiply each distance by some number to get them to the same number

Answer 8

i guess? I don't really understand this

Answer 9

let's say for instance the answer is B (it's not, but let's say it is)

Rectangle ABCD by 2 and Rectangle PQRS by 3 to create congruent rectangle of dimensions 3 x 2 units

so we would multiply the distance of 8 by 2 to get 16

then multiply the distance of 4 by 3 to get 12

but 16 doesn't equal 12, so that's why B isn't the answer

Answer 10

ohh okay so let me try A Rectangle ABCD by 1/2 and Rectangle PQRS by 2 to create congruent rectangles of dimensions 4 x 3 units

Answer 11

8*1/2=4
4*2=8 so it's not A/

Answer 12

yep

8*(1/2) = 4

4*2 = 8

doesn't work (4 = 8 is false)

Answer 13

C Rectangle ABCD by 1/4 and Rectangle PQRS by 4 to create congruent rectangles of dimensions 4 x 3 units

Answer 14

8*1/4=2
4*4=16

Answer 15

no right?

Answer 16

correct, that doesn't work either

Answer 17

D Rectangle ABCD by 1/4 and Rectangle PQRS by 1/2 to create congruent rectangles of dimensions 2 x 3 units

Answer 18

is it D?

Answer 19

8*(1/4) = 2

4*(1/2) = 2

works (2 = 2 is true)

Answer 20

so because can show it's true and we've eliminated everything else, it has to be D

Answer 21

yay! thank you :D

Answer 22

yw