Question

25
quadrilateral efgh
will be dilated by a
scale factor of 3 to
create quadrilateral
efgh. if the
coordinates of vertex
f of quadrilateral
efgh are (21, 9), what
are the coordinates of
vertex g?
a (21, 9)
b (9, 3)
c (15, 0)
d (12, 12)

Explanation:

Step1: Find original F coordinates

From the graph, vertex $F$ has coordinates $(7, 3)$.

Step2: Verify dilation rule

Given $F'(21, 9)$, check scale factor: $\frac{21}{7}=3$, $\frac{9}{3}=3$. Dilation rule: $(x,y)\to(3x,3y)$.

Step3: Find original G coordinates

From the graph, vertex $G$ has coordinates $(5, 0)$.

Step4: Calculate G' coordinates

Apply dilation rule: $3\times5=15$, $3\times0=0$. So $G'(15,0)$.

Answer:

C. (15, 0)