Question

polygon wxyz has vertices w(4, 2), x(6, 4), y(3, 3), and z(4, 5). polygon wxyz is a dilation of wxyz with center of dilation (0, 0) and vertex coordinates w(2, 1), x(3, 2), y(1.5, 1.5), and z(2, 2.5). find the scale - factor of the dilation. enter the correct answer in the box. scale factor□ show hints

Explanation:

Step1: Recall dilation formula

For a dilation with center $(0,0)$, if a point $(x,y)$ is dilated to $(x',y')$, the scale - factor $k$ is given by $x' = kx$ and $y'=ky$. Let's take one of the corresponding points, say $W(4,2)$ and $W'(2,1)$.

Step2: Calculate scale - factor for x - coordinates

Using the formula $x' = kx$, substituting $x = 4$ (co - ordinate of $W$) and $x'=2$ (co - ordinate of $W'$), we get $2=k\times4$. Solving for $k$, we have $k=\frac{2}{4}=\frac{1}{2}$.

Step3: Verify with y - coordinates

Using the formula $y' = ky$, substituting $y = 2$ (co - ordinate of $W$) and $y' = 1$ (co - ordinate of $W'$), we get $1=k\times2$. Solving for $k$, we have $k=\frac{1}{2}$.

Answer:

$\frac{1}{2}$