Chapter 4: Q3. (page 178)

Write a translation matrix that moves $Δ D E F$ up and left on the coordinate plane.

Short Answer

Expert verified

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

Step by step solution

- Vertex matrix

Let $(a_{1}, a_{2})$ be an ordered pair then its vertex matrix will be $[\begin{matrix} a_{1} \\ a_{2} \end{matrix}]$

- Vertex matrix for a triangle

As a triangle has 3 ordered pair on vertices so required matrix has 2 rows and 3 columns. If $(d_{1}, d_{2}), (e_{1}, e_{2}), and (f_{1}, f_{2})$ are coordinates of $Δ D E F$ then its vertex matrix will be localid="1648727656737" $[\begin{matrix} d_{1} & e_{1} & f_{1} \\ d_{2} & e_{2} & f_{2} \end{matrix}]$

- Write general translation matrix

Let the matrix is translated to xunits left then x is subtracted from first row and let the matrix is translated to yunits up then yis added from second row.

Thus translation matrix is of the form

$[\begin{matrix} - x & - x & - x \\ y & y & y \end{matrix}]$

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Write a translation matrix that moves $Δ D E F$ up and left on the coordinate plane.

Short Answer

Step by step solution

- Vertex matrix

- Vertex matrix for a triangle

- Write general translation matrix

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Write a translation matrix that moves ΔDEFup and left on the coordinate plane.

Short Answer

Step by step solution

- Vertex matrix

- Vertex matrix for a triangle

- Write general translation matrix

One App. One Place for Learning.

Most popular questions from this chapter

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Write a translation matrix that moves $Δ D E F$ up and left on the coordinate plane.