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)
please im about to cri

Answer 1

Answer:

(a) Side lengths

$RS = \sqrt{5}$     $ST = \sqrt{17}$    $RT = \sqrt{18}$

(b) Slope

$RS = \frac{1}{2}$      $RT = 1$      $ST = -4$

(c) Scalene triangle

Step-by-step explanation:

Given

$R = (2,3)$

$S = (4,4)$

$T = (5,0)$

Solving (a): Length of each side

This is calculated using distance formula

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

So, we have:

$RS = \sqrt{(4 - 2)^2 + (4 - 3)^2}$

$RS = \sqrt{5}$

$ST = \sqrt{(5 - 4)^2 + (0- 4)^2}$

$ST = \sqrt{17}$

$RT = \sqrt{(5 - 2)^2 + (0 - 3)^2}$

$RT = \sqrt{18}$

Solving (b): The slope of each side

This is calculated using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$RS = \frac{4- 3}{4- 2}$

$RS = \frac{1}{2}$

$RT = \frac{0 - 3}{5- 2}$

$RT = \frac{ - 3}{- 3}$

$RT = 1$

$ST = \frac{0 - 4}{5- 4}$

$ST = \frac{- 4}{1}$

$ST = -4$

Solving (c): Classify the triangle

In (a), we have:

$RS = \sqrt{5}$

$ST = \sqrt{17}$

$RT = \sqrt{18}$

None of the sides are equal;

The triangle is scalene