Mathematics, 13.07.2021 21:50 editsa

(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.

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Answer from: sdxnessa

Part A

The length of side $\overline {RS}$ is √5 units

The length of side $\overline {ST}$ is √17 units

The length of side $\overline {TR}$ is √18 units

Part B

The slope of side $\overline {RS}$ is (1/2)

The slope of side $\overline {ST}$ is -4

The slope of side $\overline {TR}$ 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;

$d = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

∴ The length of side $\overline {RS}$ = √((4 - 3)² + (4 - 2)²) = √5

The length of side $\overline {RS}$ = √5

The length of side $\overline {ST}$ = √((0 - 4)² + (5 - 4)²) = √17

The length of side $\overline {ST}$ = √17

The length of side $\overline {TR}$ = √((3 - 0)² + (2 - 5)²) = √18

The length of side $\overline {TR}$ = √18

Part B

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

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$The \ slope \ of \ side \ \overline {RS} , m_1 = \dfrac{4 - 3}{4 - 2} = \dfrac{1}{2}$

The slope of side $\overline {RS}$ , m₁ = (1/2)

$The \ slope \ of \ side \ \overline {ST} , m_2 = \dfrac{0 - 4}{5 - 4} = -4$

The slope of side $\overline {ST}$ , m₂ = -4

$The \ slope \ of \ side \ \overline {TR}, m_3 = \dfrac{3 - 0}{2 - 5} = -1$

The slope of side $\overline {TR}$ , 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

Answer from: Quest

answer: you have to send a photo of the question

step-by-step explanation:

Answer from: Quest

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.

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(04.01 MC) Triangle RST has vertices located at R (2, 3), S (4, 4), and T (5, 0). Part A: Find the l...