Question

TECHNOLOGY

For exercise 35 and 36, use the following information.

As you move the mouse for your computer, a corresponding arrow is translated on the screen. Suppose the position of the cursor on the screen is given in inches with the origin at the bottom left-hand corner of the screen.

35. You want to move the cursor 3 inches to the right and 4 inches up. Write a translation matrix that can be used to move the cursor to the new position.

Short answer

The translation matrix is $\left[\begin{array}{c}3\\ 4\\ \end{array}\right]$

Step-by-step solution

- Write general translation matrix

An ordered pair is represented by a column matrix.

If the matrix is translated to x units right or left then x is added or subtracted from first row respectively.

If the matrix is translated to y units up or down then y is added or subtracted from second row respectively.

Thus translation matrix for an ordered pair is of the form

$\left[\begin{array}{c}x\\ y\\ \end{array}\right]$

- Find value of x and y

As the triangle is translated 3 inches right, so $x=3$

As the triangle is translated 4 inches up, so $y=4$

- Find translated matrix

Substitute 3 for x and 4 for y in general translated matrix gives required matrix

$\left[\begin{array}{c}3\\ 4\\ \end{array}\right]$