Lyndsey’s advertising firm is working on a project for one of its customers. Lyndsey is asked to move a figure in the advertisement. The new figure must be similar to the old figure. The change is shown in the graph. Write a series of transformations that Lyndsey can use to move the old figure to the new figure. Explain why the figures are similar. *

Step-by-step explanation:

Since, old figure is the dilated form of the new figure.

For the dilation of the old figure to new by a scale factor 's',

s = =

Rule for the dilation of a point by a scale factor 'k',

(x, y) → k(x, y)

        → (kx, ky)

If the vertices of the old triangle are dilated by a scale factor of ,

Coordinates of the dilated triangle of the old triangle will be,

A(3, 4) → A'(, 2)

B(3, 8) → B'(, 4)

C(5, 4) → C'(, 2)

Now these points are rotated by an angle of 90° counterclockwise about the origin,

Rule for the rotation is,

(x, y) → (-y, x)

→ A"(-2, )

B'(, 4) → B"(-4,

C'(, 2) → C"(-2,

Further these points have been reflected across x-axis,

A"(-2, ) → P(-2, -)

B"(-4, ) → Q(-4, -)

C"(-2, ) → R(-2, -)

Therefore, old triangle is dilated by a scale factor of , followed by rotation of 90° counterclockwise about the origin and then reflected across x-axis to form the new triangle.

4+4+2x

or

2x+8

step-by-step explanation: