Use matrices to determine the coordinates of the vertices of the reflected figure. then graph the pre-image and the image on the same coordinate grid.

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)

Step-by-step explanation:

* Lets study the matrices of the reflection

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

- 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

- 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' is (-3 , -7)

∵ Point S is (5 , 3)

∴

∴ S' is (5 , -3)

∵ Point T is (6 , -5)

∴

∴ 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)

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour =

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second=   which is the required answer.