Question

Pre-image ​ ABCD is dilated to be image ​ A′B′C′D′ ​ . The origin is the center of dilation.

What scale factor is used to create the dilation?

Answer 1

2

Explanation:

ABCD is 3 by 2 and A'B'C'D' is 6 by 4

Answer 2

From the given figure;

Coordinates of Pre-Image ABCD are:

A(1, 4) ,B(3, 4), C(3, 1) and D(1, 1)

and

Coordinates of Image A'B'C'D' are;

A'(2, 8), B'(6, 8), C'(6, 2) and D'(2, 2)

The rule of dilation with scale factor k and centered at origin is given by;

`(x, y) \rightarrow (kx, ky)`

Consider any coordinates:

Take A (1, 4) and A'(2, 8) to find the values of k;

Using above rules:

`A(1, 4) \rightarrow (k(1), k(4))= A'(k, 4k)`

A'(k, 4k) = A'(2, 8)

Compare both sides we have

k = 2

Therefore, the scale factor(k) is used to create the dilation is 2