SOLUTION: In triangle XYZ, X_1, Y_1, and Z_1 are the midpoints of $\overline{YZ},$ $\overline{XZ},$ and $\overline{XY},$ respectively. A dilation maps $X$ to $Y$ with scale factor 3. A seco

Question 1209348: In triangle XYZ, X_1, Y_1, and Z_1 are the midpoints of $\overline{YZ},$ $\overline{XZ},$ and $\overline{XY},$ respectively. A dilation maps $X$ to $Y$ with scale factor 3. A second dilation maps $Y$ to $Z_1$ with scale factor 5. When both dilations are combined, what is the overall scale factor?

Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

The problem has a flaw/typo.

Let's say X and Y are at locations (1,1) and (3,3) in that order.
A dilation with scale factor 3 will get us from X to Y.

Z₁ is the midpoint of X and Y.
This places Z₁ at (2,2)
To go from Y to Z₁, we need to apply the scale factor 2/3 (not 5)

If we applied scale factor 5 to point Y then we'd go from (3,3) to (15,15)
You'll have to ask your teacher if s/he made a typo.

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