Question

1. the coordinates of △abc and its image are shown. describe the transformation.

a(1, 2)→a( - 1, 2)
b(3, 3)→b( - 3, 3)
c( - 1, 5)→c(1, 5)

1. the coordinates of △xyz and its image are shown. describe the transformation.

x(0, - 3)→x(0, 3)
y( - 2, - 4)→y( - 2, 4)
z( - 1, 2)→z( - 1, - 2)

Explanation:

Step1: Analyze coordinates of ΔABC

For each point in ΔABC, the y - coordinate remains the same and the x - coordinate changes sign. For example, for point A(1, 2) to A'(-1, 2), x = 1 changes to x=-1 and y = 2 stays the same. This is the rule for reflection over the y - axis: (x,y)→(-x,y).

Step2: Analyze coordinates of ΔXYZ

For each point in ΔXYZ, the x - coordinate remains the same and the y - coordinate changes sign. For example, for point X(0, - 3) to X'(0, 3), x = 0 stays the same and y=-3 changes to y = 3. This is the rule for reflection over the x - axis: (x,y)→(x,-y).

Answer:

1. Reflection over the y - axis.
2. Reflection over the x - axis.