Chapter 4: Q4. (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.
4. Write the translation matrix.

Short Answer

Expert verified

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

Step by step solution

- Write general translation matrix

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.

If the matrix is translated to x units right or left then x is added or subtracted from first row respectively.

If the matrix is translated to y units up or down then y is added or subtracted from second row respectively.

Thus translation matrix is of the form

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

- Find value of x and y

As the triangle is translated 3 units right, so $x = 3$

As the triangle is translated 1 unit down, so $y = - 1$

- Find translated matrix

Substitute 3 forx and $- 1$ for y in general translated matrix gives required matrix

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

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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.
4. Write the translation matrix.

Short Answer

Step by step solution

- Write general translation matrix

- Find value of x and y

- Find translated matrix

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Triangle ABC with vertices A1,4,B2,-5,andC-6,-6 is translated 3 units right and 1 unit down.4. Write the translation matrix.

Short Answer

Step by step solution

- Write general translation matrix

- Find value of x and y

- Find translated matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Statistics

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Pure 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.
4. Write the translation matrix.