Answer:
The coordinates of the vertices of the reflected figure are :
R' is (3 , 7), S' is (-7 , 2), T' is (-5 , -3) ⇒the right answer is figure (d)
Step-by-step explanation:
* Lets study the matrices of the reflection
- The matrix of the reflection across the x-axis is
[tex]\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right][/tex]
- 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
[tex]\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right][/tex]
- 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 y-axis
by each point to find the image of each point
- The dimension of the matrix of the reflection across the y-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' = [tex]\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right] \left[\begin{array}{ccc}-3\\7\end{array}\right]=[/tex]
[tex]\left[\begin{array}{ccc}(-1)(-3)+(0)(7)\\(0)(-3)+(1)(7)\end{array}\right]=\left[\begin{array}{ccc}3\\7\end{array}\right][/tex]
∴ R' is (3 , 7)
∵ Point S is (7 , 2)
∴ S' = [tex]\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]\left[\begin{array}{ccc}2\\7\end{array}\right]=[/tex]
[tex]\left[\begin{array}{ccc}(-1)(7)+(0)(2)\\(0)(7)+(1)(2)\end{array}\right]=\left[\begin{array}{ccc}-7\\2\end{array}\right][/tex]
∴ S' is (-7 , 2)
∵ Point T is (5 , -3)
∴ T' = [tex]\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]\left[\begin{array}{ccc}5\\-3\end{array}\right]=[/tex]
[tex]\left[\begin{array}{ccc}(-1)(5)+(0)(-3)\\(0)(5)+(1)(-3)\end{array}\right]=\left[\begin{array}{ccc}-5\\-3\end{array}\right][/tex]
∴ T' is (-5 , -3)
* Look to the answer and find the correct figure
- In figure (d) R' is (3 , 7), S' is (-7 , 2), T' is (-5 , -3)
∴ The right answer is figure (d)
