Question

rules
original points: a (-1, 4) b (-2, -3) c (3, -3)
new points: a (-2, 8) b (-4, -6) c (6, -6)
when calculating the scale factor...
if __ then figure is __
if __ then figure is __
example
triangle abc is dilated by a scale factor of ____

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ for dilation of a point $(x,y)$ to $(x',y')$ is given by $k=\frac{x'}{x}=\frac{y'}{y}$ (assuming $x
eq0$ and $y
eq0$).

Step2: Calculate scale factor using point A

For point A with original coordinates $(-1,4)$ and new coordinates $(-2,8)$. Calculate the scale factor for the x - coordinates: $k_x=\frac{-2}{-1}=2$, and for the y - coordinates: $k_y=\frac{8}{4}=2$.

Step3: Confirm with other points

For point B with original coordinates $(-2,-3)$ and new coordinates $(-4,-6)$. The scale factor for x - coordinates: $k_x=\frac{-4}{-2}=2$, and for y - coordinates: $k_y=\frac{-6}{-3}=2$. For point C with original coordinates $(3,-3)$ and new coordinates $(6,-6)$. The scale factor for x - coordinates: $k_x=\frac{6}{3}=2$, and for y - coordinates: $k_y=\frac{-6}{-3}=2$.

Answer:

2