Question

after dilating a point $(3,5)$ by a factor of 3, what will its new coordinates be?
a. $(3,5)$
b. $(6,10)$
c. $(9,15)$
d. $(12,20)$

Explanation:

Step1: Recall dilation rule

To dilate a point $(x,y)$ by a scale factor $k$, multiply each coordinate by $k$: $(x \times k, y \times k)$

Step2: Apply scale factor to coordinates

Original point: $(3,5)$, scale factor $k=3$.
New $x$-coordinate: $3 \times 3 = 9$
New $y$-coordinate: $5 \times 3 = 15$

Answer:

c. (9,15)