Chapter 4: Q57. (page 188)

For exercises 56-58, use the following information
The vertices of $Δ A B C$ are $A (- 2, 1), B (1, 2), and C (2, - 3)$ . The triangle is dilated so that its perimeter is $2 \frac{1}{2}$ times the original perimeter.
57. Find the coordinates of the image $Δ A' B' C'$

Short Answer

Expert verified

Coordinates of the image after a dilation by a scale factor of $2 \frac{1}{2}$ are $A' (- 5, 2 \frac{1}{2}), B' (2 \frac{1}{2}, 5), and C' (5, - 7 \frac{1}{2})$

Step by step solution

- Vertex matrix of ΔABC

Vertex matrix of coordinates of given triangle is $[\begin{matrix} - 2 & 1 & 2 \\ 1 & 2 & - 3 \end{matrix}]$

- Vertex matrix after dilation

Vertex matrix of triangle after dilation is product of scale factor with vertex matrix of given triangle as shown below

2 \frac{1}{2} \times [\begin{matrix} - 2 & 1 & 2 \\ 1 & 2 & - 3 \end{matrix}] = [\begin{matrix} - 5 & 2 \frac{1}{2} & 5 \\ 2 \frac{1}{2} & 5 & - 7 \frac{1}{2} \end{matrix}]

- Coordinates of image after dilation

As, each coordinate is represented by a column of vertex matrix, so each column represents one coordinate.

Thus, coordinates of image after dilation are

$A' (- 5, 2 \frac{1}{2}), B' (2 \frac{1}{2}, 5), and C' (5, - 7 \frac{1}{2})$

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For exercises 56-58, use the following information
The vertices of $Δ A B C$ are $A (- 2, 1), B (1, 2), and C (2, - 3)$ . The triangle is dilated so that its perimeter is $2 \frac{1}{2}$ times the original perimeter.
57. Find the coordinates of the image $Δ A' B' C'$

Short Answer

Step by step solution

- Vertex matrix of ΔABC

- Vertex matrix after dilation

- Coordinates of image after dilation

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For exercises 56-58, use the following informationThe vertices of ΔABCare A-2,1,B1,2,andC2,-3. The triangle is dilated so that its perimeter is 212 times the original perimeter.57. Find the coordinates of the image ΔA'B'C'

Short Answer

Step by step solution

- Vertex matrix of ΔABC

- Vertex matrix after dilation

- Coordinates of image after dilation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Decision Maths

Geometry

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

For exercises 56-58, use the following information
The vertices of $Δ A B C$ are $A (- 2, 1), B (1, 2), and C (2, - 3)$ . The triangle is dilated so that its perimeter is $2 \frac{1}{2}$ times the original perimeter.
57. Find the coordinates of the image $Δ A' B' C'$