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?

- anonymous

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- anonymous

@jim_thompson5910

- jim_thompson5910

the figure is missing

- anonymous

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- jim_thompson5910

what is point D?

- anonymous

-2?

- jim_thompson5910

as an ordered pair, where is point D?

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

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

- jim_thompson5910

then you go to the left 1 unit
then you go up 4 units to get to the point ________

- anonymous

D

- anonymous

wait, then you go left 1 after what?

- jim_thompson5910

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)

- anonymous

okay then I scale it by the factor of 2?

- jim_thompson5910

yes but first tell me where point D is

- jim_thompson5910

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

- anonymous

-3,4?

- jim_thompson5910

close, but it's (-1, 4)
you go over to the left 1, then up 4

- anonymous

no.. nevermind.

- jim_thompson5910

D is the point (-1,4)

- anonymous

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

- jim_thompson5910

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

- anonymous

Okay it was what I though it was.

- anonymous

Could you check my answer on another question?

- jim_thompson5910

sure what do you need

- anonymous

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

- anonymous

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

- jim_thompson5910

do you remember the distance formula?

- anonymous

distance formula for what?

- anonymous

I think so..

- jim_thompson5910

for finding the distance between two points

- jim_thompson5910

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

- anonymous

I don't know... ?

- jim_thompson5910

use the distance formula
\[\large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}\]
to find out

- anonymous

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

- jim_thompson5910

show me what you got so far

- anonymous

do I use just one coordinate pair at a time?

- jim_thompson5910

you use them both

- jim_thompson5910

(x1,y1) is the first point
(x2,y2) is the second point

- anonymous

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

- jim_thompson5910

you do them a pair at a time

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

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?

- anonymous

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

- jim_thompson5910

so far, so good

- jim_thompson5910

now simplify/evaluate

- anonymous

Okay..can you check

- jim_thompson5910

what did you get

- anonymous

20

- jim_thompson5910

good

- jim_thompson5910

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)

- anonymous

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

- jim_thompson5910

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

- jim_thompson5910

yes you need to find the width now

- anonymous

ok one sec

- anonymous

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

- jim_thompson5910

yes it does, keep going

- anonymous

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

- jim_thompson5910

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

- jim_thompson5910

it should be this
d = sqrt( 16^2 + 12^2 )
d = sqrt( 256 + 144 )
d = sqrt( 400 )
d = 20

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

correct on both

- jim_thompson5910

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

- anonymous

How do I get the other two?

- jim_thompson5910

find the distance from G to H

- anonymous

Why not F to I?

- jim_thompson5910

that's another side length we'll get to

- anonymous

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.

- jim_thompson5910

good

- jim_thompson5910

how about from F to I

- anonymous

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.

- jim_thompson5910

very good

- jim_thompson5910

now add up the 4 sides to get the perimeter

- anonymous

the perimeter is 50 units

- jim_thompson5910

perfect

- anonymous

thank you!!

- jim_thompson5910

you're welcome

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