Dilation Math Example 4

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

hard

After a dilation from the origin, point

Q(3, 5)

maps to

Q'(7.5, 12.5)

. Find the scale factor

k

. Then determine by what factor the area of any figure changes under this dilation.

1
Step 1: $k = Q'_x / Q_x = 7.5/3 = 2.5$ . Verify: $k = 12.5/5 = 2.5$ . ✓
2
Step 2: Under dilation with scale factor $k$ , all lengths scale by $k$ , so area scales by $k^2 = 2.5^2 = 6.25$ .

Answer

k = 2.5

; area scales by a factor of

6.25

The scale factor is found by dividing any image coordinate by the corresponding original coordinate. Since area is two-dimensional, it scales by

k^2

. A dilation with

k = 2.5

makes every area

6.25

times larger.

About Dilation

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

Triangle [formula] has vertices [formula], [formula], [formula]. Apply a dilation from the origin wi

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