Question

Triangle RST has vertices located a R (2,3), S (4,4), and T (5,0)part A: Find the length of each side of the Triangle. show the work Part B: Find the slope of each side of the Triangle. show the workPart C: classify the Triangle. explain your reasoning

Answer 1

Answer:

Scalene Triangle

Explanation:

The vertices of triangle RST are:

$R(2,3),S(4,4),and\; T(5,0)$

Part A

Use the distance formula to find the length of each side.

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

(a)R(2,3) and S (4,4)

$\begin{gathered} RS=\sqrt[]{(4-2)^2+(4-3)^2} \\ =\sqrt[]{2^2+1^2} \\ =\sqrt[]{5} \end{gathered}$

(b)R (2,3)and T (5,0)

$\begin{gathered} RT=\sqrt[]{(5-2)^2+(0-3)^2} \\ =\sqrt[]{3^2+3^2} \\ =\sqrt[]{18} \\ =3\sqrt[]{2} \end{gathered}$

(c)S (4,4), and T (5,0)

$\begin{gathered} ST=\sqrt[]{(5-4)^2+(0-4)^2} \\ =\sqrt[]{1^2+4^2} \\ =\sqrt[]{17} \end{gathered}$

Part B

$\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}$

(a)Slope of line RS: R(2,3) and S (4,4)

$\text{Slope of RS}=\frac{4-3}{4-2}=\frac{1}{2}$

(b)Slope of line RT: R(2,3) and T(5,0)

$\text{Slope of RT}=\frac{0-3}{5-2}=\frac{-3}{3}=-1$

(c)Slope of line ST: S(4,4) and T(5,0)

$\text{Slope of ST}=\frac{0-4}{5-4}=\frac{-4}{1}=-4$

Part C

We observe that the three side lengths of the triangle are unequal.

Therefore, the triangle is a Scalene Triangle.