Question

NEED HELP FINDING SOME COORDINATES

Answer 1

Answer:

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

Step-by-step 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.

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

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