Question

Point $A(7,3)$ is translated to $A\text{'}(16,-9)$

Which rule describes the transformation?

Answer 1

Find the transformation:

Given a point $A(7,3).$

This point is translated by a value. Let the value be $\left(x,y\right)$

And after application of translation

The position of the new point is $A\text{'}(16,-9)$

In Mathematical terms this can be given as follows:

$\left(7,3\right)+\left(x,y\right)=\left(16,-9\right)$

This addition is done coordinate wise.

Therefore the equation are as follows:

$$\begin{gathered} 7+x=16\left(1\right) \\ 3+y=-9\left(2\right) \end{gathered}$$

Solve the equation to get the values of x we get,

$$\begin{gathered} 7+x=16 \\ \Rightarrow x=16-7 \\ \Rightarrow x=9 \end{gathered}$$

Similarly on solving second equation we get,

$$\begin{gathered} 3+y=-9 \\ \Rightarrow y=-9-3 \\ \Rightarrow y=-12 \end{gathered}$$

Therefore, the translated vector is $\left(9,-12\right).$