I NEED THIS ASAP!!!
Triangle ABC has vertices located at A( 0, 2), B (2, 5), and C (−1, 7).

Part A: Find the length of each side of the triangle. Show your work. (4 points)

Part B: Find the slope of each side of the triangle. Show your work. (3 points)

Part C: Classify the triangle. Explain your reasoning.

[tex]m_{\overline{AB}}=\frac{5-2}{2-0}=\frac{3}{2} \\ \\ m_{\overline{AC}}=\frac{7-2}{-1-0}=-5 \\ \\ m_{\overline{BC}}=\sqrt{7-5}{-1-2}=-\frac{2}{3}[/tex]

Part C

The slopes of AB and BC are negative reciprocals of each other, so the triangle is a right triangle.

Also, AB = BC, meaning the triangle is isosceles.

Therefore, the triangle is a right isosceles triangle.

xero099 xero099 · Answer 2 · 2022-08-23T16:42:39+02:00

A) The lengths of the sides are AB = √13, BC = √13 and m = - 1 / 5.

B) The slopes of the sides are m = 3 / 2, m = - 2 / 3 and m = - 1 / 5.

C) The given triangle is an 45 - 45 - 90 right isosceles triangle (AB = BC, AB ⊥ BC).

How to analyze and classify a triangle by its sides and angles

Triangles are figures generated by three non-colinear points on a Cartesian plane. In the first part of this problem we have to determine the lengths of each side by Pythagorean theorem:

Side AB

AB = √[(2 - 0)² + (5 - 2)²]

AB = √13

Side BC

BC = √[(-1 - 2)² + (7 - 5)²]

BC = √13

Side AC

AC = √[(- 1 - 0)² + (7 - 2)²]

AC = √25

The slope of each side is determined by the secant line formula:

Side AB

m = [5 - 2] / [2 - 0]

m = 3 / 2

Side BC

m = [7 - 5] / [- 1 - 2]

m = - 2 / 3

Side AC

m = [- 1 - 0] / [7 - 2]

m = - 1 / 5

Lastly, we find that the given triangle is an 45 - 45 - 90 right isosceles triangle (AB = BC, AB ⊥ BC).

To learn more on triangles: https://brainly.com/question/2773823

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