Question

What is the mage of point D in figure ABCD for a dilation with a center of (0,0) and a scale factor of 2?

Answer 1

@jim_thompson5910

Answer 2

the figure is missing

Answer 3

what is point D?

Answer 4

-2?

Answer 5

as an ordered pair, where is point D?

Answer 6

ie what are the coordinates of it? or its location?

Answer 7

I don't know... that's why I'm asking for help.

Answer 8

well you start at (0,0), which is the origin

Answer 9

then you go to the left 1 unit

then you go up 4 units to get to the point ________

Answer 10

D

Answer 11

wait, then you go left 1 after what?

Answer 12

yes but where is point D

ex: if you went to the right 1 and up 3, then you would be at the point (1,3)

Answer 13

okay then I scale it by the factor of 2?

Answer 14

yes but first tell me where point D is

Answer 15

what is the (x,y) form of this point

Answer 16

-3,4?

Answer 17

close, but it's (-1, 4)

you go over to the left 1, then up 4

Answer 18

no.. nevermind.

Answer 19

D is the point (-1,4)

Answer 20

yeah.. I was looking at point A for one of the coordinates

Answer 21

when you apply the scale factor of 2, you double each coordinate

Answer 22

Okay it was what I though it was.

Answer 23

Could you check my answer on another question?

Answer 24

sure what do you need

Answer 25

What is the perimeter of the rectangle with vertices F(-6,-10), G(10,2), H(7,6), and I(-9,-6)? My answer:

Answer 26

2(w + h)
2(-6 + -10) = -32
2(10 + 2) = 24
2(7 + 6) = 26
(-9 + -6) = -30

Answer 27

do you remember the distance formula?

Answer 28

distance formula for what?

Answer 29

I think so..

Answer 30

for finding the distance between two points

Answer 31

for instance, what is the distance from point F to point G?

Answer 32

I don't know... ?

Answer 33

use the distance formula

\[\large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}\]

to find out

Answer 34

I don't feel like I'm inputting it correctly.

Answer 35

show me what you got so far

Answer 36

do I use just one coordinate pair at a time?

Answer 37

you use them both

Answer 38

(x1,y1) is the first point

(x2,y2) is the second point

Answer 39

yes.. but how can that work when there are 4 pairs of coordinates?

Answer 40

you do them a pair at a time

Answer 41

so if you want to find the distance from F to G, you only focus on those two points

Answer 42

can you input an example? I don't think you're understanding my question

Answer 43

Let's make point F the first point

so that means

F(-6,-10) = (x1,y1)

which means

x1 = -6
y1 = -10

see how I'm getting this?

Answer 44

d = sqrt(-6-10)^2 + (-10-2)^2?

Answer 45

so far, so good

Answer 46

now simplify/evaluate

Answer 47

Okay..can you check

Answer 48

what did you get

Answer 49

20

Answer 50

good

Answer 51

so that is the length of one side

luckily the opposite side is also 20 because this a rectangle (opposite sides of a rectangle are equal)

Answer 52

okay.. now the same thing for the other coordinates?

Answer 53

so you can think of it as the length of 20 units

Answer 54

yes you need to find the width now

Answer 55

ok one sec

Answer 56

d = sqrt(7-(-9)^2 + (6-(-6))^2
look okay for the first step?

Answer 57

yes it does, keep going

Answer 58

d = sqrt(x2-x1)^2 + (y2-y1)^2
d = sqrt(7-(-9)^2 + (6-(-6))^2
d = sqrt(16)^2 + (12)^2
d = sqrt(256)^2 + (144)^2
d = sqrt(65,536)+(20,736)
d = sqrt(86,272)
d = 293.720956
rounded: 293.7

Answer 59

you're doing great until you hit this line d = sqrt(65,536)+(20,736)

Answer 60

it should be this

d = sqrt( 16^2 + 12^2 )

d = sqrt( 256 + 144 )

d = sqrt( 400 )

d = 20

Answer 61

so the distance from point H to point I is 20 units

Answer 62

ohhh hahaha whoops okay so from H to I is 20 and f to g is 20?

Answer 63

correct on both

Answer 64

you just need two more sides

once you have the length of all 4 sides, you can add them up to get the perimeter

Answer 65

How do I get the other two?

Answer 66

find the distance from G to H

Answer 67

Why not F to I?

Answer 68

that's another side length we'll get to

Answer 69

d = sqrt(x2-x1)^2 + (y2-y1)^2
d = sqrt(10-7)^2 + (2-6)^2
d = sqrt(3)^2 + (-4)^2
d = sqrt(9) + (16)
d= sqrt(25)
d = 5

The distance from G to H is 5 units.

Answer 70

good

Answer 71

how about from F to I

Answer 72

d = sqrt(x2-x1)^2 + (y2-y1)^2
d = sqrt(-6-(-9))^2 + (-10-(-6))^2
d = sqrt(3)^2 + (-4)^2
d = sqrt(9) + (16)
d = sqrt(25)
d = 5

The distance from F to I is 5 units.

Answer 73

very good

Answer 74

now add up the 4 sides to get the perimeter

Answer 75

the perimeter is 50 units

Answer 76

perfect

Answer 77

thank you!!

Answer 78

you're welcome