Use matrices to determine the coordinates of the vertices of the rotated figure. then graph the pre-image and the image of the same coordinate grid. (pictureprovided)

The coordinates of the vertices of the rotated figure are :

U' (1 , -6), V' (-8 , -4), W' (-5 , 7) ⇒ the right answer is figure (d)

Step-by-step explanation:

* Lets study the matrices of the Rotation by 180°  

- When we rotate a point around the origin by 180° clockwise

 or anti-clockwise, we change the sign of the x-coordinate and

 the y-coordinate of the point

- Then matrix of the rotation 180° is

* Now lets solve the problem

- We will multiply the matrix of the rotation  by each point to

 find the image of each point

- The dimension of the matrix of the rotation  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 U is (-1 , 6)

∴

∴ U' = (1 , -6)

∵ Point V is (8 , 4)

∴

∴ V' = (-8 , -4)

∵ Point W is (5 , -7)

∴

∴ W' = (-5 , 7)

* Now look to the figures to find the right answer

∵ The images of the points are U' (1 , -6), V' (-8 , -4), W' (-5 , 7)

∴ The right answer is figure (d)

i do not know this sorry : (

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !