Question

1. is it true or false that the green quadrilateral below is a dilation of the pink quadrilateral by a factor of $\frac{5}{3}$? (-5,4) (-3,4) (-5,2) (0,2) (-5,-2) (-1,-2) (-5,-5) (5,-5) true false

Explanation:

Step1: Recall dilation rule

For a dilation about the origin with scale - factor $k$, if a point $(x,y)$ is dilated, the new point is $(kx,ky)$. Let's check the distance between corresponding points of the two quadrilaterals. Consider the horizontal side of the pink quadrilateral from $x=-5$ to $x = - 3$, length $l_1=|-3-(-5)| = 2$. The corresponding horizontal side of the green quadrilateral from $x=-5$ to $x=-1$, length $l_2=|-1 - (-5)|=4$.

Step2: Calculate scale - factor for horizontal side

The ratio of the lengths of the corresponding horizontal sides is $\frac{l_2}{l_1}=\frac{4}{2}=2
eq\frac{5}{3}$.

Answer:

false