Question

asked Aug 9, 2020 215k views

1 Answer

Nathan Getachew · Answer 1 · 2020-08-13T03:59:56+0000

Answer:

The coordinates of the vertices of the reflected figure are :

R' is (-3 , -7), S' is (5 , -3), T' is (6 , 5) ⇒the right answer is figure (a)

Explanation:

* Lets study the matrices of the reflection

- The matrix of the reflection across the x-axis is

$\left[\begin{array}{cc}1&0\\0&-1\end{array}\right]$

- Because when we reflect any point across the x-axis we

change the sign of the y-coordinate

- The matrix of the reflection across the y-axis is

$\left[\begin{array}{cc}-1&0\\0&1\end{array}\right]$

- Because when we reflect any point across the y-axis we

change the sign of the x-coordinate

* Now lets solve the problem

- We will multiply the matrix of the reflection across the x-axis

by each point to find the image of each point

- The dimension of the matrix of the reflection across the x-axis

is 2×2 and the dimension of the matrix of each point is 2×1,

then the dimension of the matrix of each image is 2×1

∵ Point R is (-3 , 7)

∴
$R'=\left[\begin{array}{cc}1&0\\0&-1\end{array}\right]\left[\begin{array}{c}-3\\7\end{array}\right]=$

$\left[\begin{array}{c}(1)(-3)+(0)(7)\\(0)(-3)+(-1)(7)\end{array}\right]=\left[\begin{array}{c}-3\\-7\end{array}\right]$

∴ R' is (-3 , -7)

∵ Point S is (5 , 3)

∴
$S'=\left[\begin{array}{cc}1&0\\0&-1\end{array}\right]\left[\begin{array}{c}5\\3\end{array}\right]=$

$\left[\begin{array}{c}(1)(5)+(0)(3)\\(0)(5)+(-1)(3)\end{array}\right]=\left[\begin{array}{c}5\\-3\end{array}\right]$

∴ S' is (5 , -3)

∵ Point T is (6 , -5)

∴
$T'=\left[\begin{array}{cc}1&0\\0&-1\end{array}\right]\left[\begin{array}{c}6\\-5\end{array}\right]=$

$\left[\begin{array}{c}(1)(6)+(0)(-5)\\(0)(6)+(-1)(-5)\end{array}\right]=\left[\begin{array}{c\pi }6\\5\end{array}\right]$

∴ T' is (6 , 5)

* Look to the answer and find the correct figure

- In figure (d) R' is (-3 , -7), S' is (5 , -3), T' is (6 , 5)

∴ The right answer is figure (a)

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