Similar Shapes Are Dilations

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?

• A'(9,9) B'(18,18) C'(27,9)

• A'(6,6) B'(9,9) C'(12,6)

• A'(0,0) B'(3,3) C'(6,0)

• A'(1,1) B'(2,2) C'(3,1)

Is this an enlargement or reduction? (blue = original image)

• reduction

• enlargement

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.

• B' (2 , 4.5)

• B' (-8 ,-18)

• B' (8 ,18)

• B' (9 ,4)

In a dilation what mathematical operation is used with the scale factor?

• addition 

• subtraction 

• multiplication 

• division 

Suppose a triangle with the vertices A(–2, 4), B(–1, –3), and C(4, –2) were dilated, with the center of dilation at the origin and with a scale factor of 2. What will be the coordinates of C'?

• (2, -1)

• (8, -4)

• (8, 4)

• (2, 1)

a transformation that ​changes the size (enlargement or reduction) of a figure is called a ​ ​ ​ (a)  

• dilation

• rotation

• reflection

• translation

Michael and Grace have a triangle with vertices A(–2, 4), B(–1, –3), and C(4, –2). If they dilate this triangle from the origin with a scale factor of 2, what are the new coordinates of C'?

• (2, -1)

• (8, -4)

• (8, 4)

• (2, 1)

Answer explanation

To find C' after dilation, multiply the coordinates of C(4, -2) by the scale factor of 2. Thus, C' = (4*2, -2*2) = (8, -4). Therefore, the correct answer is (8, -4).

A triangle has vertices with coordinates (2,0), (3, -1) and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?

• (5,3), (6,2), (1,-2)

• (6,0), (9,-3), (-6,-15)

• (2/3,0), (1,-1/3), (-2/3,-5/3)

• (-1,-3), (0,-4), (-5,-8)

If a shape is dilated, is the new image congruent or similar to its preimage?

• congruent

• similar

The only transformation that changes the length of sides is dilation.

• True

• False