Question

NEED HELP FINDING SOME COORDINATES

Answer 1

The image of
`(7,2)` is
`(2,12)`

Explanation:

First you need to find the translation vector.

Let the translation vector be
`u=(a,b)`. Then the translation rule is

`(x,y)\to (x+a,y+b)`.

From the equation, the image of
`P(2,-4)` is
`P'(-3,6)`.When we apply this rule using the translation vector, we get

`P(2,-4)\to P'(2+a,-4+b)`

Now we have

`P'(2+a,-4+b)=P'(-3,6)`

We can therefore equate corresponding coordinates

`2+a=-3` and
`-4+b=6`

This implies that:

`a=-3-2` and
`b=6+4`

`a=-5` and
`b=10`

Hence our translation vector is
`u=(-5,10)`

The translation rule now becomes:

`(x,y)\to (x-5,y+10)`.

To find the image of (7,2), we plug it into the translation rule.

`(7,2)\to (7-5,2+10)`.

`(7,2)\to (2,12)`.