Question

1. on a coordinate plane, vertex a for triangle abc is located at (6,4). triangle abc is dilated by a scale factor of \\(\frac{1}{2}\\) with the center of dilation at the origin. the resulting image is triangle abc. what are the coordinates of vertex a? a.) (3, 2) b.) (12, 8) c.) (5.5, 3.5) d.) (6.5, 4.5)

Explanation:

Step1: Recall dilation rule for origin

When dilating a point $(x,y)$ with scale factor $k$ centered at the origin, the new coordinates are $(k \cdot x, k \cdot y)$.

Step2: Apply scale factor to point A

Given $A=(6,4)$ and $k=\frac{1}{2}$, calculate new coordinates:
$x' = \frac{1}{2} \cdot 6 = 3$
$y' = \frac{1}{2} \cdot 4 = 2$

Answer:

A.) (3, 2)