Dilations Review

CAT ≅ DOG

$$\frac{CA}{DO}=\frac{AT}{OG}=\frac{TC}{GO}$$

CAT∼DOG

∠C = ∠G

The area of the largest sign is three times the area of the smaller sign.

The perimeter of the larger sign is three times the perimeter of the smaller sign.

The perimeter of the larger sign is nine times the perimeter of the smaller sign.

The area of the smaller sign is nine times the area of the larger sign.

$$(x,y)\ \rightarrow\ (x,-y)$$

$$(x,y)\ \rightarrow\ (x+4,y-1)$$

$$(x,y)\ \rightarrow\ (4x,4y)$$

$$\left(x,y\right)\ \rightarrow\ \left(y,-x\right)$$

$$(x,y)\ \rightarrow\ (2x,2y)$$

$$\left(x,y\right)\ \rightarrow\ \left(\frac{1}{2}x,\ y\right)$$

$$\left(x,y\right)\ \rightarrow\ \left(x-1,\ y-4\right)$$

$$\left(x,y\right)\ \rightarrow\ \left(\frac{1}{2}x,\ \frac{1}{2}y\right)$$

If $$a<1$$ , then the image of XYZ is larger than the pre-image.

If $$a=1$$ , then the image of XYZ is larger than the pre-image.

If $$a>1$$ , then the image of XYZ is smaller than the pre-image.

If $$a<1$$ , then the image of XYZ is smaller than the pre-image.

$$\Delta A'B'C'\ \cong\ \Delta ABC$$

$$\frac{AB}{A'B'}=\frac{BC}{B'C'}=\frac{CA}{C'A'}$$

$$\frac{BC}{B'C'}=\frac{CA}{C'B'}=\frac{CB}{C'A'}$$

$$A'A=B'B=C'C$$

(28, -28)

(14, -14)

(4, 21)

(9, 10)

The angle measures of ABC are less than than the angle measures of triangle A'B'C'.

The side lengths of ABC are $$\frac{1}{4}$$ ​ as long as the side lengths of A'B'C'.

The angle measures of A'B'C' are less than the angle measures of ABC.

The side lengths of A'B'C' are $$\frac{1}{4}$$ as long as the side lengths of ABC.

A reflection across the x-axis

A translation 7 units down

A dilation by a scale factor of 5

A rotation of $$90\degree\ clockwise$$

12

16

4

8