Question

Figure AAA is a scale image of figure BBB.

Figure AAA maps to figure BBB with a scale factor of 2\dfrac{1}{2}2
2
1
​
2, start fraction, 1, divided by, 2, end fraction.
What is the value of xxx?

Answer 1

Dilation involves changing the size and the position of a shape

The value of x is 20

The scale factor from A to B is given as:

$k = \frac 12$

The corresponding side lengths of both figures are:

• Side length x on figure A and side length of 10 units on figure B

So, we have:

$\frac{10}{x} = k$

Substitute 1/2 for k

$\frac{10}{x} = \frac{1}{2}$

Cross multiply the above equation

$x \times 1 = 10 \times 2$

Multiply 2 by 10

$x \times 1 =20$

Multiply 1 and x

$x =20$

Hence, the value of x is 20

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