(04.01 MC) 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. Part B: Find the slope of each side of the triangle. Show your work. Part C: Classify the triangle. Explain your reasoning.

Part A

The length of side is √5 units

The length of side is √17 units

The length of side is √18 units

Part B

The slope of side is (1/2)

The slope of side is -4

The slope of side is -1

Part C

The triangle is a scalene triangle

Step-by-step explanation:

The given vertices of the triangle ΔRST are; R(2, 3), S(4, 4), T(5, 0)

Part A

The length of each side is found by using the formula for the distance, d, between two points given their coordinates (x₁, y₁), (x₂, y₂) as follows;

∴ The length of side = √((4 - 3)² + (4 - 2)²) = √5

The length of side = √5

The length of side = √((0 - 4)² + (5 - 4)²) = √17

The length of side = √17

The length of side = √((3 - 0)² + (2 - 5)²) = √18

The length of side = √18

Part B

The slope, m, of each side of the triangle is given as follows;

The slope of side , m₁ = (1/2)

The slope of side , m₂ = -4

The slope of side , m₃ = -1

Part C

The class of the triangle is a scalene triangle

Given that the length of the sides of the triangle are all unequal, the triangle is a scalene triangle

Given that the square of the length of the longest side, √18, is not equal to the sum of the squares of the lengths of the other two sides, the triangle is not a right triangle

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w