Question

what is the scale factor that would be used to dilate ▱math to ▱math , from the origin, if the coordinates include m(-10, 2) → m(-5, 1) and t(-2, -4) → t(-1, -2)

Explanation:

Step1: Recall scale - factor formula

For a dilation from the origin, if a point $(x,y)$ is dilated to $(x',y')$, the scale factor $k$ can be found by $k=\frac{x'}{x}=\frac{y'}{y}$.

Step2: Calculate scale - factor using point M

For point $M(-10,2)$ dilated to $M'(-5,1)$, calculate $k$ using the $x$ - coordinates: $k=\frac{-5}{-10}=\frac{1}{2}$. Calculate $k$ using the $y$ - coordinates: $k = \frac{1}{2}$.

Step3: Confirm with point T

For point $T(-2,-4)$ dilated to $T'(-1,-2)$, using the $x$ - coordinates, $k=\frac{-1}{-2}=\frac{1}{2}$. Using the $y$ - coordinates, $k=\frac{-2}{-4}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$