Question

DKLM ~ PTRS

DRAW the diagram on your own paper, and LABEL each side with the information below:
MD = 20, DK = 6z+6, KL = 8w+1, LM = 40, PT = 12, TR= 4w - 2, RS = 16
What is the scale factor / reference ratio if DKLM is the preimage (old) and PTRS is the image (new)?
Write a simplified fraction in lowest terms, in the form a/b.

Answer 1

The scale factor if DKLM is the old and PTRS is the image as a simplified fraction in its lowest terms is 5/2

What is the scale factor if DKLM is the old and PTRS is the image?

Scale factor is the ratio between the scale of a given original object and a new object.

MD = 20,

DK = 6z+6,

KL = 8w+1,

LM = 40,

PT = 12,

TR= 4w - 2,

RS = 16

LM : RS

= 40 : 16

= 40/16

= 5/2

So,

DK : PT = 5 : 2

6z+6 : 12 = 5 : 2

(6z + 6) / 12 = 5/2

cross product

2(6z + 6) = 12 × 5

12z + 12 = 60

12z = 60 - 12

12z = 48

z = 48/12

z = 4

Also,

KL : TR =

(8w+1) : (4w - 2) = 5 : 2

(8w+1) / (4w - 2) = 5/2

cross product

2(8w +1) = 5(4w - 2)

16w + 2 = 20w - 10

16w - 20w = -10 - 2

-4w = -12

w = -12/-4

w = 3