Question

Triangle RST has vertices located at R (2, 3), S (4,4), and T (5,0).
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)

Answer 1

Vertices of the triangle located at R(2, 3), S(4, 4), T(5, 0), gives;

Part A:

The lengths of the sides are;

• RS = √5
• RT = 3•√2
• ST = √(17)

Part B;

The slopes are;

• Slope of RS = 1/2
• Slope of RT = -1
• Slope of ST = 4

Part C:

• The triangle is a scalene triangle

Which method can be used to analyze the triangle?

Part A: The length of each side can be found using Pythagorean theorem as follows;

Length of RS = √((4 - 2)²+(4 - 3)²) = √5

Length of RT = √((5 - 2)²+(0 - 3)²) = 3•√2

Length of ST = √((4 - 5)²+(4 - 0)²) = √(17)

Part B:

The slope of each side are;

• Slope of RS = (4 - 3)/(4 - 2)= 1/2

• Slope of RT = (0 - 3)/(5 - 2) = -1

• Slope of ST = (4 - 0)/(4 - 5) = 4

Part C: Given that the length of the sides of the triangle are different, (√5, 3•√2, and √(17)), the triangle is a scalene triangle, by definition of scalene triangles.

Learn more about the types of triangles here:

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