Question

5
triangle abc will
be dilated by a scale
factor of 4 to create
triangle abc. if the
coordinates of vertex
a of triangle abc
are (8, 16), what are
the coordinates of
vertex b?
a (8, 4)
c (4, 8)
b (4, 4)
d (8, 8)

Explanation:

Step1: Find original A coordinates

From the graph, vertex A is at $(2, 4)$.

Step2: Verify dilation rule

Dilation scale factor $k=4$. For a point $(x,y)$, dilation gives $(kx, ky)$. Check: $4\times2=8$, $4\times4=16$, which matches $A'(8,16)$.

Step3: Find original B coordinates

From the graph, vertex B is at $(1, 1)$.

Step4: Calculate B' coordinates

Apply dilation: $x=4\times1=4$, $y=4\times1=4$.

Answer:

B. (4, 4)