Question

1. dilate point a(3, - 4) by a scale factor of k = 3 with the center of dilation at the origin. what are the coordinates of a?

a. (3, - 3)
b. (9, - 12)
c. (1, - 1.33)
d. (9, - 9)

Explanation:

Step1: Recall dilation formula

When dilating a point $(x,y)$ by a scale factor $k$ with the center of dilation at the origin, the new - point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Identify the values of $x$, $y$, and $k$

Here, $x = 3$, $y=-4$, and $k = 3$.

Step3: Calculate the new coordinates

$x'=k\cdot x=3\times3 = 9$ and $y'=k\cdot y=3\times(-4)=-12$.

Answer:

The coordinates of $A'$ are $(9, - 12)$ (Option b).