Question

JK has length 10. J’K’ is a dilation of JK and has endpoints J (5, 16) and K (12, -8). Find the scale factor of the dilation and show your work. Is the dilation an enlargement or a reduction? How do you know?

Answer 1

The scale factor for the dilation from JK to J'K' is 2.5, computed by dividing the length of the dilated segment (25 units) by the original length (10 units). Since the scale factor is greater than 1, the dilation is an enlargement.

Step-by-step explanation:

The length of JK has been given as 10. The coordinates of the dilated line segment J'K' are J' (5, 16) and K' (12, -8). To find the scale factor of the dilation, we first calculate the length of J'K' using the distance formula:

d = √[(x2-x1)² + (y2-y1)²]

Inserting the coordinates of J' and K', the distance d becomes:

d = √[(12-5)² + (-8-16)²] = √[49 + 576] = √[625]

d = 25

Since J'K' is 25 units long and JK is 10 units long, the scale factor is the ratio of J'K' to JK:

Scale factor = J'K' / JK = 25 / 10 = 2.5

As the scale factor is greater than 1, this dilation is an enlargement.