Question

1. triangle abc is shown on the coordinate plane below. the triangle is dilated from the origin. identify the coordinates of the dilated triangle abc. 3. the triangle abc has coordinates a(6, 1), b(12, 4), and c(-6, 2). the triangle is dilated from the origin by factor r = \frac{1}{2}. identify the coordinates of the dilated triangle abc.

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated from the origin by a scale - factor $r$, the new coordinates $(x',y')$ are given by $x'=r\times x$ and $y'=r\times y$.

Step2: Find coordinates of $A'$

Given $A(6,1)$ and $r = \frac{1}{2}$, then $x_{A'}=\frac{1}{2}\times6 = 3$ and $y_{A'}=\frac{1}{2}\times1=\frac{1}{2}$. So $A'(3,\frac{1}{2})$.

Step3: Find coordinates of $B'$

Given $B(12,4)$ and $r=\frac{1}{2}$, then $x_{B'}=\frac{1}{2}\times12 = 6$ and $y_{B'}=\frac{1}{2}\times4 = 2$. So $B'(6,2)$.

Step4: Find coordinates of $C'$

Given $C(-6,2)$ and $r=\frac{1}{2}$, then $x_{C'}=\frac{1}{2}\times(-6)=-3$ and $y_{C'}=\frac{1}{2}\times2 = 1$. So $C'(-3,1)$.

Answer:

$A'(3,\frac{1}{2}), B'(6,2), C'(-3,1)$