Question

1 graph rhombus stuv with s(-6, 2), t(2, 8), u(10, 2), v(2, -4) and its image after a dilation of 1/2. what are the coordinates of v? a) (4, -8) b) (4, 8) c) (1, -2) d) (1, 1) e) (1/2, -2)

Explanation:

Step1: Recall dilation formula

For a dilation with scale - factor $k$ centered at the origin, if a point $(x,y)$ is dilated, the new point $(x',y')$ has coordinates $(kx,ky)$. Here, the scale - factor $k = \frac{1}{2}$, and the original point $V$ has coordinates $(2,-4)$.

Step2: Calculate new $x$ - coordinate

$x'=k\times x=\frac{1}{2}\times2 = 1$.

Step3: Calculate new $y$ - coordinate

$y'=k\times y=\frac{1}{2}\times(-4)=-2$.
So the coordinates of $V'$ are $(1, -2)$.

Answer:

C. (1, -2)