Chapter 4: Q5. (page 178)

Triangle $A B C$ with vertices $A (1, 4), B (2, - 5), and C (- 6, - 6)$ is translated 3 units right and 1 unit down.
Find the coordinates of $Δ A' B' C'$

Short Answer

Expert verified

Coordinates of $Δ A' B' C'$ are $A' (4, 3), B' (5, - 6), and C' (- 3, - 7)$

Step by step solution

- Write vertex matrix of ΔABC

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 localid="1648219790093" $[\begin{matrix} 1 & 2 & - 6 \\ 4 & - 5 & - 6 \end{matrix}]$

- Write translation matrix

As the triangle is translated 3 units right and 1 unit down so translation matrix is

$[\begin{matrix} 3 & 3 & 3 \\ - 1 & - 1 & - 1 \end{matrix}]$

- Write vertex matrix of ΔA'B'C'

Sum of vertex matrix of $Δ A B C$ with translation matrix gives vertex matrix of $Δ A' B' C'$

localid="1648219819556" $[\begin{matrix} 1 & 2 & - 6 \\ 4 & - 5 & - 6 \end{matrix}] + [\begin{matrix} 3 & 3 & 3 \\ - 1 & - 1 & - 1 \end{matrix}] = [\begin{matrix} 4 & 5 & - 3 \\ 3 & - 6 & - 7 \end{matrix}]$

- Find coordinates of ΔA'B'C'

As, each coordinate is represented by a column of vertex matrix, so each column represents one coordinate of triangle $A' B' C'$

Coordinates are $A' (4, 3), B' (5, - 6), and C' (- 3, - 7)$

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Triangle $A B C$ with vertices $A (1, 4), B (2, - 5), and C (- 6, - 6)$ is translated 3 units right and 1 unit down.
Find the coordinates of $Δ A' B' C'$

Short Answer

Step by step solution

- Write vertex matrix of ΔABC

- Write translation matrix

- Write vertex matrix of ΔA'B'C'

- Find coordinates of ΔA'B'C'

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Triangle ABCwith vertices A1,4,B2,-5,andC-6,-6is translated 3 units right and 1 unit down.Find the coordinates of ΔA'B'C'

Short Answer

Step by step solution

- Write vertex matrix of ΔABC

- Write translation matrix

- Write vertex matrix of ΔA'B'C'

- Find coordinates of ΔA'B'C'

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Statistics

Pure Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Triangle $A B C$ with vertices $A (1, 4), B (2, - 5), and C (- 6, - 6)$ is translated 3 units right and 1 unit down.
Find the coordinates of $Δ A' B' C'$