Q36. - Algebra 2

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.

36. If the cursor is currently at $\left(3.5,2.25\right)$, what are the coordinates of the position after the translation?

Step-by-Step Solution

Answer

Coordinates of the position after translation is $\left[\begin{array}{c}6.5\\ 6.25\end{array}\right]$

Step 1 - Write vertex matrix of given point

For the coordinate $\left(x,y\right)$, vertex matrix is $\left[\begin{array}{c}x\\ y\\ \end{array}\right]$. So for coordinate $\left(3.5,2.25\right)$, vertex matrix will be $\left[\begin{array}{c}3.5\\ 2.25\\ \end{array}\right]$

Step 2 - Write translation matrix

As the point is translated 3 units right and 4 units up so translation matrix is$\left[\begin{array}{c}3\\ 4\\ \end{array}\right]$

Step 3 - Write vertex matrix of image point

Sum of vertex matrix of given point with translation matrix gives vertex matrix of image point

$\left[\begin{array}{c}3.5\\ 2.25\\ \end{array}\right]+\left[\begin{array}{c}3\\ 4\\ \end{array}\right]=\left[\begin{array}{c}6.5\\ 6.25\\ \end{array}\right]$

Step 4 - Find coordinates of position after translation

As, each coordinate is represented by a column of vertex matrix, so each column represents one coordinate 

Coordinate of position after translation is $\left[\begin{array}{c}6.5\\ 6.25\\ \end{array}\right]$