BONUS: Graph triangle ABC with vertices A(7, -2), B(8, -5), C(3, -8) and its image after the following transformations. Give the coordinates of the final image. (a) Translation: (x, y) → (x – 9, y + 10)

(b) Rotation: 270° counterclockwise about the origin

(c) Reflection: in the line y = -x

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west

well, because the $0.25 is an added cost depending on how many minutes, the answer would be y = 30 + 0.25x.