Question

13 multiple choice 1 point find the perimeter of a triangle with vertices a(3, 1), b(2, -1), and c(-3, 2). leave your answer in decimal form, rounded to the nearest hundredth. 15 units 7.58 units 14.15 units 18.92 units

Explanation:

Step1: Calculate length of AB

Use distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$\overline{AB}=\sqrt{(2-3)^2+(-1-1)^2}=\sqrt{(-1)^2+(-2)^2}=\sqrt{1+4}=\sqrt{5}\approx2.236$

Step2: Calculate length of BC

Apply distance formula to B, C
$\overline{BC}=\sqrt{(-3-2)^2+(2-(-1))^2}=\sqrt{(-5)^2+(3)^2}=\sqrt{25+9}=\sqrt{34}\approx5.831$

Step3: Calculate length of AC

Apply distance formula to A, C
$\overline{AC}=\sqrt{(-3-3)^2+(2-1)^2}=\sqrt{(-6)^2+(1)^2}=\sqrt{36+1}=\sqrt{37}\approx6.083$

Step4: Sum lengths for perimeter

Add the three side lengths
$\text{Perimeter}\approx2.236+5.831+6.083=14.15$

Answer:

14.15 units