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

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

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

Answer 2

@amistre64

Answer 3

start by centering both rectangles at the origin if they arent yet

Answer 4

might start with a corner, then readjust

Answer 5

lets corner them at the origin first

Rectangle ABCD – A(0, 8), B(8, 8), C(8, -4), D(0, -4)
-8 -8 -8 -8
---------------------------
0 0 8 0 8 -12 0 -12


Rectangle PQRS – P(0, 4), Q(4, 4), R(4, -2), S(0, -2)
-4 -4 -4 -4
--------------------------
0 0 4 0 4 -6 0 -6

Answer 6

now to center them


0 0 8 0 8 -12 0 -12
^ ^ ^ ^
w = 8 so -4 h = -12 so +6
-------------------------------
-4 6 4 6 4 -6 -4 -6



0 0 4 0 4 -6 0 -6
^ ^ ^ ^
w = 4 so -2 h = -6 so +3
---------------------------------
-2 3 2 3 2 -3 -2 -3

Answer 7

now all we have to do is compare a set of similar corners:

-4 6 to -2 3

Answer 8

is there anything else?

Answer 9

only thing left to do is to compare the options with these 2 points to see what fits ... im a little offput by the doubles: by 1 by 2; means what?

Answer 10

is it the first answer????

Answer 11

........or the last answer....

Answer 12

i cant read the options .... they have double speak in them that is muddling things up

Answer 13

Rectangle ABCD by 1 by 4 and Rectangle PQRS by 1 by 2 to create congruent rectangles of dimensions 2 x 3 units........is this the answer?

Answer 14

what does: by 1 by 4 mean ?????

Answer 15

... by 1/4 and ... by 1/2 maybe?

Answer 16

idk here are the answers

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

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

Answer 17

well, if you cant read the options, and i cant make sense of them ... then we are at a stand still

Answer 18

reposting the same muddled jargon over and over again is NOT clarifying the issue ....

Answer 19

the best i can determine is:

n(4,6) = k(2,3

4n = 2k when n/k = 1/2

Answer 20

the only thing that might make a lick of sense out ofthe options, would then be the last one ...

Answer 21

ok thanks

Answer 22

yep ...