7(2x - 8) = -2x + 8
2 answers:
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Answer:
The coordinates of the vertices of the reflected figure are :
R' is (5 , -2) , S' is (3 , 5) , T' is (-7 , 6) ⇒ the right answer is (d)
Step-by-step explanation:
* When you reflect a point across the line y = x, the x-coordinate
and y-coordinate change their places.
- If the point is (x , y) then its image is (y , x)
* If you reflect over the line y = -x, the x-coordinate and y-coordinate
change their places and their signs
- If the point is (x , y) then its image is (-y , -x)
* Lets study the matrix of the reflection about the line y = x
- The matrix of the reflection about the line y = x is
- Because the x-coordinate and y-coordinate change places.
* Now lets solve the problem
- We will multiply the matrix of the reflection about y = x
by each point to find the image of each point
- The dimension of the matrix of the reflection about y = x
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
∵ The point R is (-2 , 5)
∴
∴ R' is (5 , -2)
∵ The point S is (5 , 3)
∴
∴ S' is (3 , 5)
∵ The point T is (6 , -7)
∴
∴ T' is (-7 , 6)
* Lets look to the figures to find the right answer
∵ The R' is (5 , -2) , S' is (3 , 5) , T' is (-7 , 6)
∴ The right answer is (d)