Chapter 9.2, Problem 30HP

To determine

To find: The final image of a point that is translated along $\left(x+a,y+b\right)$ and then $\left(x+c,y+d\right)$ .

Answer to Problem 30HP

The coordinates of the final image are $\langle x+a+c,y+b+d\rangle$ .

Explanation of Solution

Given information:

The given information is $\left(x+a,y+b\right)$ and $\left(x+c,y+d\right)$ .

Calculation:

This is the same as translating along $\left(a,b\right)$ then translating along $\left(c,\text{d}\right)$ .

For the first translation, we have:

  $\left(x+a,y+b\right)$

For the second translation, we have

  $\begin{array}{l}\langle \left(x+a\right)+c,\left(y+b\right)+d\rangle \\ \langle x+a+c,y+b+d\rangle \end{array}$

Therefore, the coordinates of the final image are $\langle x+a+c,y+b+d\rangle$ .