Question

Nancy drew parallelogram ABCD as shown.



On the same grid she will draw parallelogram PQRS similar to parallelogram ABCD with the ratio of corresponding side lengths PQ and AB equal to 4 : 1. If the coordinates of vertex P are (-8, -5), what could be the coordinates of vertex Q?

Answer 1

Let's not go overboard!

Answer 2

Did they give choices?

Answer 3

when they say PQRS is similar to ABCD, this means the same shape, but bigger (or smaller)
PQ to AB = 4:1 means PQ is 4 times longer than AB

Answer 4

(8, -5)
(4, 6)
(0, -5)
(-4, -1)

Answer 5

so the first step, is how long is AB?

Answer 6

You don't even need the distance formula (though it would work). Just count

Answer 7

so what do i count?

Answer 8

You need to find how long AB is. The number of units to move to get from A to B

Answer 9

distance between (4,6) and (8,6)

Answer 10

why those coordinates?

Answer 11

On the same grid she will draw parallelogram PQRS similar to parallelogram ABCD with the ratio of corresponding side lengths PQ and AB equal to 4 : 1.

Answer 12

this is a long-winded way of say PQ is 4 times longer than AB

So the first thing to do is find how long AB is. I looked at your picture, and saw A=(4,6) and B is (8,6)

Answer 13

the distance between them is 4

Answer 14

so how long is PQ going to be?

Answer 15

PQ:AB is 4:1 means PQ is 4 times longer, or 4*4= 16 units long.

Now we need to find a point 16 units distant from P
coordinates of vertex P are (-8, -5),

Answer 16

4,6

Answer 17

So you are saying the distance from P (-8,-5) to (4,6) = 16?

d^2 = (4 - -8)^2 + (6 - -5)^2 = 12^2+11^2 = 144+121=265
d= sqrt(d^2) = sqrt(265) = 16.28
close, but not close enough

Answer 18

Is this too hard?

Answer 19

im working on it but yeah it's pretty hard

Answer 20

AHHA it's 0,-5

Answer 21

nvm i was think way ahead and missed somthing. or am i right?