PLS HELP BRAINLEIST AND 25 POINTS 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. (3 points)

Given:

The vertices of a triangle ABC are A( 0, 2), B (2, 5), and C (−1, 7).

To find:

Part A: The length of each side of the triangle.

Part B: The slope of each side of the triangle.

Part C: Classify the triangle.

Solution:

Part A: The vertices of a triangle ABC are A( 0, 2), B (2, 5), and C (−1, 7).

Distance formula:

Using the distance formula, we get

Similarly,

And,

Therefore, the length of each side of the triangle are .

Part B:

Slope formula:

Slope of side AB is:

Slope of side BC is:

Slope of side AC is:

Therefore, the slopes of sides AB, BC, AC are respectively.

Part C:

Product of slopes of AB and BC is:

So, side AB and BC are perpendicular to each other.

Two sides of triangle ABC are equal and one angle is a right angle.

Therefore, the triangle ABC is an isosceles right triangle.

Step-by-step explanation:

A( 0, 2), B (2, 5), and C (−1, 7)

(A) The distance formula is given by

length of side AB

Length of side BC

Length of side CA

(B) The slope of a line is given by

Slope of line AB =

Slope of line BC =

Slope of line CA =

(c) As the slope of line AB is negative of reciprocal of line BC, and length AB is equal to length BC so the triangle is right angled isosceles triangle.

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step-by-step explanation:

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