Question

2 triangle s and triangle l are scaled copies of one another.
a what is the scale factor from s to l?
b what is the scale factor from l to s?
c triangle m is also a scaled copy of s. the scale factor from s to m is \\(\frac{3}{2}\\). what is the scale factor from m to s?

Explanation:

Part (a)

Step 1: Determine base lengths of S and L

Assume grid units: Base of S is 2 units, base of L is 6 units.

Step 2: Calculate scale factor (S to L)

Scale factor = $\frac{\text{Length of L}}{\text{Length of S}}$ = $\frac{6}{2}$ = 3.

Step 1: Use reciprocal of S to L scale factor

Scale factor from L to S is reciprocal of scale factor from S to L.

Step 2: Calculate scale factor (L to S)

Scale factor = $\frac{1}{3}$ (since scale factor S to L is 3).

Step 1: Recall scale factor reciprocal property

If scale factor from S to M is $k$, scale factor from M to S is $\frac{1}{k}$.

Step 2: Calculate scale factor (M to S)

Given $k = \frac{3}{2}$, so scale factor = $\frac{1}{\frac{3}{2}}$ = $\frac{2}{3}$.

Answer:

3

Part (b)