Question

15 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. 18.92 units 7.58 units 14.15 units 15 units

Explanation:

Step1: Use distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of AB

For points $A(3,1)$ and $B(2,-1)$, $d_{AB}=\sqrt{(2 - 3)^2+(-1 - 1)^2}=\sqrt{(-1)^2+(-2)^2}=\sqrt{1 + 4}=\sqrt{5}\approx2.24$.

Step3: Calculate length of BC

For points $B(2,-1)$ and $C(-3,2)$, $d_{BC}=\sqrt{(-3 - 2)^2+(2+ 1)^2}=\sqrt{(-5)^2+3^2}=\sqrt{25 + 9}=\sqrt{34}\approx5.83$.

Step4: Calculate length of AC

For points $A(3,1)$ and $C(-3,2)$, $d_{AC}=\sqrt{(-3 - 3)^2+(2 - 1)^2}=\sqrt{(-6)^2+1^2}=\sqrt{36+1}=\sqrt{37}\approx6.08$.

Step5: Calculate perimeter

Perimeter $P=d_{AB}+d_{BC}+d_{AC}\approx2.24 + 5.83+6.08 = 14.15$.

Answer:

C. 14.15 units