Chapter 4: Q12. (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.
12. Write the translation matrix.

Short Answer

Expert verified

The translation matrix is $[\begin{matrix} - 4 & - 4 & - 4 \\ 2 & 2 & 2 \end{matrix}]$

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 4 units left, so $x = - 4$

As the triangle is translated 2 units op, so $y = 2$

- Find translated matrix

Substitute $- 4$ for x and 2 for y in general translated matrix gives required matrix

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

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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.
12. 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 DEF with vertices D1,4,E2,-5,andF-6,-6 is translated 4 units left and 2 units up.12. 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

Theoretical and Mathematical Physics

Pure Maths

Calculus

Logic and Functions

Statistics

Probability and 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.
12. Write the translation matrix.