Chapter 4: Q2. (page 194)

For Exercises 1-3, reflect square ABCDEwith vertices $A (1, 2)$ , $B (4, - 1)$ , $C (1, - 4)$ and $D (- 2, - 1)$ over the y-axis.
2. Find the coordinates of $A' B' C' D'$ .

Short Answer

Expert verified

The coordinates of $A' B' C' D'$ are: $A' (- 1, 2)$ , $B' (- 4, - 1)$ , $C' (- 1, - 4)$ and . $D' (2, - 1)$

Step by step solution

- Description of step.

The vertex matrix for the square is given by:

$[\begin{matrix} 1 & 4 & 1 & - 2 \\ 2 & - 1 & - 4 & - 1 \end{matrix}]$

- Description of step.

As, the given square $A B C D$ is to be reflected over the Y-axis, therefore multiply the matrix $[\begin{matrix} - 1 & 0 \\ 0 & 1 \end{matrix}]$ on the left with the vertex matrix for the squareABCD to get the vertex matrix for square $A' B' C' D'$ .

Therefore, it can be obtained that:

$\begin{matrix} [\begin{matrix} - 1 & 0 \\ 0 & 1 \end{matrix}] \cdot [\begin{matrix} 1 & 4 & 1 & - 2 \\ 2 & - 1 & - 4 & - 1 \end{matrix}] = [\begin{matrix} - 1 + 0 & - 4 + 0 & - 1 + 0 & 2 + 0 \\ 0 + 2 & 0 - 1 & 0 - 4 & 0 - 1 \end{matrix}] \\ = [\begin{matrix} - 1 & - 4 & - 1 & 2 \\ 2 & - 1 & - 4 & - 1 \end{matrix}] \end{matrix}$

- Description of step.

Therefore, the coordinates of $A' B' C' D'$ are: $A' (- 1, 2)$ , $B' (- 4, - 1)$ , $C' (- 1, - 4)$ and . $D' (2, - 1)$

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For Exercises 1-3, reflect square ABCDEwith vertices $A (1, 2)$ , $B (4, - 1)$ , $C (1, - 4)$ and $D (- 2, - 1)$ over the y-axis.
2. Find the coordinates of $A' B' C' D'$ .

Short Answer

Step by step solution

- Description of step.

- Description of step.

- Description of step.

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For Exercises 1-3, reflect square ABCDEwith vertices A1,2, B4,-1, C1,-4andD-2,-1 over the y-axis.2. Find the coordinates of A'B'C'D'.

Short Answer

Step by step solution

­- Description of step.

­- Description of step.

­- Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Logic and Functions

Mechanics Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

For Exercises 1-3, reflect square ABCDEwith vertices $A (1, 2)$ , $B (4, - 1)$ , $C (1, - 4)$ and $D (- 2, - 1)$ over the y-axis.
2. Find the coordinates of $A' B' C' D'$ .

- Description of step.

- Description of step.

- Description of step.