Question

Using the rules of reflections, find the new vertices of the figure reflected across the given line.1. A(2,3), B(-1,5), C(4,-1); y = x2. U(-8,2), V(-3,-1), W(3,3); y-axis 3. E(-3,-2), F(6,-4), G(-2,1); x-axis

Answer 1

1. A(2,3), B(-1,5), C(4,-1); y = x



2. U(-8,2), V(-3,-1), W(3,3); y-axis



3. E(-3,-2), F(6,-4), G(-2,1); x-axis​

Part 1

we know that

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places.

so

the rule is

(x,y) -------> (y,x)

therefore

A(2,3) ------> A'(3,2)

B(-1,5) ------> B'(5,-1)

C(4,-1) ------> C'(-1,4)

Part 2

The rule of the reflection across the y-axis is

(x,y) ----->(-x,y)

therefore

U(-8,2) ------> U'(8,2)

V(-3,-1) -----> V'(3,-1)

W(3,3) -----> W'(-3,3)

Part 3

The rule of the reflection across the x-axis is

(x,y) ------> (x,-y)

therefore

E(-3,-2) -----> E'(-3,2)

F(6,-4) ------> F'(6,4)

G(-2,1) -----> G'(-2,-1)