Chapter 4: Q13. (page 179)

Triangle $D E F$ with vertices $D (1, 4), E (2, - 5), and F (- 6, - 6)$ is translated 4 units left and 2 units up.
13. Find the coordinates of $Δ D' E' F'$

Short Answer

Expert verified

Coordinates of $Δ D' E' F'$ are $D' (- 3, 6), E' (- 2, - 3), and F' (- 10, - 4)$

Step by step solution

- Write vertex matrix of ΔDEF

Since, an ordered pair is represented by a column matrix and triangle has 3 ordered pair on vertices so required matrix has 2 rows and 3 columns.

First row represent $x - coordinate$ and second row represents $y - coordinate$ of each vertex.

Thus vertex matrix is $[\begin{matrix} 1 & 2 & - 6 \\ 4 & - 5 & - 6 \end{matrix}]$

- Write translation matrix

As the triangle is translated 4 units left and 2 units up so translation matrix is

[\begin{matrix} - 4 & - 4 & - 4 \\ 2 & 2 & 2 \end{matrix}]

- Write vertex matrix of ΔD'E'F'

Sum of vertex matrix of $Δ D E F$ with translation matrix gives vertex matrix of $Δ D' E' F'$

$[\begin{matrix} 1 & 2 & - 6 \\ 4 & - 5 & - 6 \end{matrix}] + [\begin{matrix} - 4 & - 4 & - 4 \\ 2 & 2 & 2 \end{matrix}] = [\begin{matrix} - 3 & - 2 & - 10 \\ 6 & - 3 & - 4 \end{matrix}]$

- Find coordinates of ΔD'E'F'

As, each coordinate is represented by a column of vertex matrix, so each column represents one coordinate of triangle $Δ D' E' F'$

Coordinates are $D' (- 3, 6), E' (- 2, - 3), and F' (- 10, - 4)$

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Triangle $D E F$ with vertices $D (1, 4), E (2, - 5), and F (- 6, - 6)$ is translated 4 units left and 2 units up.
13. Find the coordinates of $Δ D' E' F'$

Short Answer

Step by step solution

- Write vertex matrix of ΔDEF

- Write translation matrix

- Write vertex matrix of ΔD'E'F'

- Find coordinates of ΔD'E'F'

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Triangle DEF with vertices D1,4,E2,-5,andF-6,-6 is translated 4 units left and 2 units up.13. Find the coordinates of ΔD'E'F'

Short Answer

Step by step solution

- Write vertex matrix of ΔDEF

- Write translation matrix

- Write vertex matrix of ΔD'E'F'

- Find coordinates of ΔD'E'F'

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Triangle $D E F$ with vertices $D (1, 4), E (2, - 5), and F (- 6, - 6)$ is translated 4 units left and 2 units up.
13. Find the coordinates of $Δ D' E' F'$