Chapter 9.4, Problem 71AYU

a.

To determine

To find: the new coordinates of $\left(-3,1\right)$ if it is translated by $v=\langle -4,5\rangle$ .

Answer to Problem 71AYU

  $\left(-1,4\right)$ .

Explanation of Solution

Given:

The field of computer graphics utilize vectors to compute translation of point.

If $\left(-3,2\right)$ it is translated by $v=\langle 5,2\rangle$ , then the new coordinate is $u^{\prime }=u+v=\left(-3,2\right)$ .

Calculation:

Since the difference between two points is a vector, therefore sum of two point and a vector is a point.

  $\left(-3,1\right)+\langle -4,5\rangle =\left(-1,4\right)$ .

Hence, the new coordinates are $\left(-1,4\right)$ .

b.

To determine

To draw: the graph of given coordinates.

Explanation of Solution

Given:

The field of computer graphics utilize vectors to compute translation of point.

If $\left(-3,2\right)$ it is translated by $v=\langle 5,2\rangle$ , then the new coordinate is $u^{\prime }=u+v=\left(-3,2\right)$ .

Calculation:

Plot the vector $u\text{and}v$ .

  

Translate v to point $\left(3,-1\right)$ moving it to parallel to v.

  

Now draw the resultant vector R such that initial point R coincides with initial point of u and terminal point with $v^{\prime }$

  

Hence, the new coordinates are $\left(-1,4\right)$ .