Question

1. △rst maps to △rst. for x values: did they divide by 2 or 3 to make the pre - image x values to the image values?

pre - image\timage\tfor the y values: did they multiply by 2 or 3 to make the pre - image y values to the image values?
r(2,1) → r(1,3)
s(2, - 1) → s(1, - 3)
t(4, - 2) → t(2, - 6)
the coordinate rule is:
(x,y)→
the transformation is:
horizontal stretch when multiply to x
horizontal compression when you divide x
vertical stretch if you multiply to y value
vertical compression when you divide y

Explanation:

Step1: Analyze x - coordinate transformation

For point $R(2,1)\to R'(1,3)$, $2\div2 = 1$; for point $S(2, - 1)\to S'(1,-3)$, $2\div2=1$; for point $T(4,-2)\to T'(2,-6)$, $4\div2 = 2$. The rule for the x - coordinate is $x\to\frac{x}{2}$.

Step2: Analyze y - coordinate transformation

For point $R(2,1)\to R'(1,3)$, $1\times3 = 3$; for point $S(2,-1)\to S'(1,-3)$, $- 1\times3=-3$; for point $T(4,-2)\to T'(2,-6)$, $-2\times3=-6$. The rule for the y - coordinate is $y\to3y$.

Step3: Write the coordinate rule

Combining the x and y rules, the coordinate rule is $(x,y)\to(\frac{x}{2},3y)$.

Step4: Determine the transformation type

Since the x - coordinate is divided by 2 (horizontal compression) and the y - coordinate is multiplied by 3 (vertical stretch), the transformation is a horizontal compression by a factor of $\frac{1}{2}$ and a vertical stretch by a factor of 3.

Answer:

The coordinate rule is: $(x,y)\to(\frac{x}{2},3y)$
The transformation is: A horizontal compression by a factor of $\frac{1}{2}$ and a vertical stretch by a factor of 3.