Question

what is the perimeter of a triangle with vertices located at (-1, 4), (2, 7), and (1, 5), rounded to the nearest hundredth?

a. 8.71 units
b. 7.89 units
c. 9.24 units
d. 7.63 units

Explanation:

Step1: Calculate the distance between two points

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For points \((-1,4)\) and \((2,7)\):
\(d_1=\sqrt{(2 - (-1))^2+(7 - 4)^2}=\sqrt{3^2 + 3^2}=\sqrt{9 + 9}=\sqrt{18}\approx4.24\)

Step2: Calculate another distance

For points \((2,7)\) and \((1,5)\):
\(d_2=\sqrt{(1 - 2)^2+(5 - 7)^2}=\sqrt{(-1)^2+(-2)^2}=\sqrt{1 + 4}=\sqrt{5}\approx2.24\)

Step3: Calculate the third distance

For points \((1,5)\) and \((-1,4)\):
\(d_3=\sqrt{(-1 - 1)^2+(4 - 5)^2}=\sqrt{(-2)^2+(-1)^2}=\sqrt{4 + 1}=\sqrt{5}\approx2.76\)

Step4: Calculate the perimeter

\(P=d_1 + d_2 + d_3\approx4.24+2.24 + 2.76=9.24\)

Answer:

C. 9.24 units