Select translation, reflection, or rotation to identify the single transformation that transforms ∆pqr to ∆p'q'r'.

Part A

Represents 'Reflection'. This is so because the y-coordinates of P, Q and R remain the same in P' , Q' and R', and only the x-coordinate changes. Hence, it is reflection along the y-axis

Part B

Represents 'Rotation'. Here, the x-coordinates and y-coordinates of each of the points have changed, and the figure has been rotated clockwise around the point Q by 90°

Part C

Represents a combination of 'Translation' and 'Reflection'. Here either of the two has happened:

Part D

Represents 2 'Translations'. Here the image has been shifted by a fixed distance in both the downward direction and the right direction. Thus, it has resulted in change of both x and y coordinates.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

the answer is 24

step-by-step explanation: