Question

given the points a (3, -2), b (2, -5), and c (4, -5), classify △abc. (1 point)
○ it is an isosceles triangle.
○ it is a scalene triangle.
○ it is a right triangle.
○ it is an equilateral triangle.

Explanation:

Step1: Calculate the lengths of the sides using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For \(AB\):
\(x_1 = 3,y_1=-2,x_2 = 2,y_2=-5\)
\(AB=\sqrt{(2 - 3)^2+(-5+2)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1 + 9}=\sqrt{10}\)

For \(BC\):
\(x_1 = 2,y_1=-5,x_2 = 4,y_2=-5\)
\(BC=\sqrt{(4 - 2)^2+(-5 + 5)^2}=\sqrt{(2)^2+0^2}=2\)

For \(AC\):
\(x_1 = 3,y_1=-2,x_2 = 4,y_2=-5\)
\(AC=\sqrt{(4 - 3)^2+(-5 + 2)^2}=\sqrt{(1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}\)

Step2: Analyze the side - lengths

Since \(AB=\sqrt{10}\), \(BC = 2\), and \(AC=\sqrt{10}\), two sides (\(AB\) and \(AC\)) are equal.

Answer:

It is an isosceles triangle.