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TSI Math: Identifying the Coordinates of a Translated Shape 0 Views


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Description:

The points A (2, 1), B (0, 3), and C (-3, -1) make up ΔABC. If it is translated 5 units up and 7 units to the left, what are the coordinates of the resulting image?


Transcript

00:00

The points A at to one Be at oh three

00:05

and see at negative three Negative one Makeup angle abc

00:08

If it is translated five units up and seven units

00:11

to the left what are the coordinates of the resulting

00:14

image A translation happens when we take an image and

00:22

slide it around in a certain direction like five up

00:25

in seven left to pick this example completely at random

00:28

without changing the image itself in any way to do

00:30

this each point in the image needs to move the

00:33

same way Sort of like a round dance on one

00:35

of those cowboy barn dance thing is yeah well moving

00:38

left and right changes appoints x value while moving up

00:41

and down changes the y value right well starting with

00:43

the x value shimmy over seven units to the left

00:46

clap twice when looking at a coordinate playing the value

00:48

of x goes up A zit moves to the right

00:51

so that means it decreases when it goes the left

00:53

so subtract seven from the x value of each point

00:56

With wise they're doing the same kind of thing but

00:58

up and down the graft and the y values increases

01:00

We go up the coordinate plane so add five to

01:02

the y values at each point Well then take a

01:05

quick look at some alternate forms for writing translations like

01:08

instead of saying trends like the drug angle five units

01:11

off And seven two left We could have saved our

01:13

breath and written the following Just this you know the

01:15

x minus seven The wine plus five thinking they're well

01:18

it's the same information but written much more succinctly and

01:21

you know math Feli shrink it down even more Amp

01:23

up the math itude and write it as translation t

01:27

negative seven five minutes Very clever Okay Now start moving

01:30

the triangle around Let's Start with a which is at

01:32

two One Subtract seven from the x Value produces two

01:35

minutes Have is negative five while adding five to the

01:37

y value results in one plus five is six Well

01:40

what to call the new translated pulling at negative five

01:43

six Well we could just keep going up the alphabet

01:46

and call it d or name it harold or something

01:48

There's another and better way at a little apostrophe mark

01:51

to the original points name making it a prime and

01:54

that's how it reads kind of like you know optimist's

01:57

cousin the prime has got some transforming going on I

02:00

say we did there now move on to be do

02:02

the exact same things before two zero three Subtract seven

02:05

from accent and five toe wide and nab the point

02:07

at negative seven Eight are growing little collection here and

02:10

finally see from negative three Negative one has negative three

02:14

minus seven is naked and for Acts and then negative

02:17

1 plus five is just four for what which creates

02:19

the point See prime negative ten four hey we're all

02:22

out of points a resulting triangular image Abc prime there

02:26

has the virtue sees negative five six negative seven eight

02:29

and negative ten four and the answer is b and 00:02:32.213 --> [endTime] that's It we are shmoop

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