Question

A triangle is formed after dilating △ABC in the given figure with a scale factor of $\frac{1}{3}$, centered at the origin. The perimeter will be .

• A. 12 inches
• B. 12 inches
• C. 16 inches
• D. 10 inches

Answer 1

The correct option is A 12 inches


$\text{Coordinates of the original triangle}$
$\text{A(0,9), B(0,0), C(12,0)}$

$\text{△ABC is to be dilated with a scale factor}$
$\text{of}\frac{1}{3}.$

$\text{So, the new coordinates will be:}$
$A(0,9)=(0\times \frac{1}{3},9\times \frac{1}{3})=(0,3)\to A^{\prime }$

$B(0,0)=(0\times \frac{1}{3},0\times \frac{1}{3})=(0,0)\to B^{\prime }$

$C(12,0)=(12\times \frac{1}{3},0\times \frac{1}{3})=(4,0)\to C^{\prime }$


$\text{Perimeter of the original triangle ABC is}$
$\text{(9 + 12 + 15) inch = 36 inch}$

$\text{Perimeter of the new triangle A'B'C' is:}$
$\text{(3 + 4 + 5) inch = 12 inch}$

$\text{Perimeter of new triangle}=\frac{\text{Perimeter of original triangle}}{3}$

$\Rightarrow \text{Perimeter of new triangle}=\frac{36}{3}$
$\Rightarrow \text{Perimeter of new triangle}=12$

$\text{So, perimeter of the new triangle is}$
$\text{12 inches.}$