Question

Quadrilateral QRST is dilated by a scale factor of start fraction, 3, divided by, 4, end fraction
4
3
​
to form quadrilateral Q'R'S'T'. What is the measure of side TQ? The numbers are 15 and 30.

Answer 1

I’m missing which segment is labeled 15 and which is 30 (the preimage or the image), but the rule is:

If scale factor k takes QRST (original) to Q'R'S'T' (image), then
- image length = k × original length
- original length = image length ÷ k

Two likely interpretations:

1) If the scale factor is 3/4 and the image T'Q' = 15, then original TQ = 15 ÷ (3/4) = 15 × (4/3) = 20.

2) If the scale factor is 3/4 and the original TQ = 30, then the image T'Q' = 30 × (3/4) = 22.5.

(If the scale factor was 4/3, reverse the multiplication/division.)

Tell me which segment is 15 and which is 30 (and whether 3/4 or 4/3 is the scale), and I’ll give the exact value.