Dilation Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

Triangle

ABC

has vertices

A(2, 4)

B(6, 0)

C(4, 8)

. Apply a dilation from the origin with scale factor

k = 3

. Find the image vertices

A'

B'

C'

1
Step 1: Recall the dilation rule from the origin: $(x, y) \to (kx, ky)$ where $k$ is the scale factor.
2
Step 2: Apply to $A(2, 4)$ : $A' = (3 \cdot 2,\, 3 \cdot 4) = (6, 12)$ .
3
Step 3: Apply to $B(6, 0)$ : $B' = (3 \cdot 6,\, 3 \cdot 0) = (18, 0)$ .
4
Step 4: Apply to $C(4, 8)$ : $C' = (3 \cdot 4,\, 3 \cdot 8) = (12, 24)$ .

Answer

A'(6, 12)

B'(18, 0)

C'(12, 24)

Dilation from the origin multiplies every coordinate by the scale factor. With

k=3

the triangle is enlarged to three times its original size, keeping the same shape and orientation relative to the origin.

About Dilation

A transformation that enlarges or shrinks a figure by a scale factor from a center point.

Point [formula] is dilated from the origin with scale factor [formula]. Find the image [formula] and

Square [formula] has vertices [formula], [formula], [formula], [formula]. After a dilation from the

After a dilation from the origin, point [formula] maps to [formula]. Find the scale factor [formula]