Question

1. a triangle with vertices at a(2,3), b(5,3), and c(2,6) is transformed by the rule (x,y)→(x - 4,y + 1), then rotated 90 counter - clockwise about the origin, and finally reflected across the line y = 2. what are the coordinates of the final image of vertex a?

a) a(-4,2)
b) a(-5,6)
c) a(-4,6)
d) a(-2,5)
a) a(-4,2)
b) a(-5,6)
c) a(-4,6)
d) a(-2,5)

Explanation:

Step1: Apply translation rule

For point A(2,3), using the rule (x,y)→(x - 4,y + 1), we get A'=(2 - 4,3 + 1)=(-2,4).

Step2: Apply 90 - counter - clockwise rotation

The rule for a 90 - counter - clockwise rotation about the origin is (x,y)→(-y,x). For A'(-2,4), we have A''=(-4,-2).

Step3: Apply reflection across y = 2

The distance between y - coordinate of A'' (-2) and y = 2 is d=2-(-2)=4. The new y - coordinate after reflection across y = 2 is 2 + 4=6, and the x - coordinate remains the same. So the final point is (-4,6).

Answer:

C. A''(-4,6)