Q3. - Algebra 2

Question

Write a translation matrix that moves $\Delta DEF$ up and left on the coordinate plane.

Step-by-Step Solution

Answer

If a triangle is translated x units to the left and y units to the up then translation matrix is $\left[\begin{array}{ccc}-x& -x& -x\\ y& y& y\end{array}\right]$

Step 1 - Vertex matrix

Let $\left(a_1,a_2\right)$ be an ordered pair then its vertex matrix will be $\left[\begin{array}{c}{a}_1\\ a_2\end{array}\right]$

Step 2 - Vertex matrix for a triangle

As a triangle has 3 ordered pair on vertices so required matrix has 2 rows and 3 columns. If $\left(d_1,d_2\right),\left(e_1,e_2\right),\text{ and }\left(f_1,f_2\right)$ are coordinates of $\Delta DEF$ then its vertex matrix will be $\left[\begin{array}{ccc}{d}_1& e_1& f_1\\ d_2& e_2& f_2\end{array}\right]$

Step 3 - Write general translation matrix

Let the matrix is translated to x units left then x is subtracted from first row and let the matrix is translated to y units up then y is added from second row.

Thus translation matrix is of the form

$\left[\begin{array}{ccc}-x& -x& -x\\ y& y& y\end{array}\right]$