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.

Part B: Find the slope of each side of the triangle. Show your work.

Part C: Classify the triangle. Explain your reasoning.

Answer 1

do you know distance formula between two points?

Answer 2

A. use distance formula
B.slope of each side \[=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]
take one point=(x1,y1) and other point (x2,y2) similarly for other sides.
C.1.if product of two slopes=-1,then it is a right angled triangle and if two sides are also equalthen it is an isosceles right angled triangle.
2. if product is not =-1 and two sides are equal then it is an isosceles triangle.
3.if all the sides are equal then it is an equilateral triangle.
4.if all the sides are different then it is a scalene triangle.

Answer 3

adding onto what @surjithayer said, the distance formula is \[Distance =~ \sqrt{(x_{2} -{x_1})^2 + (y_{2} - y_{1})^2 }\]
where you have
\[ (x_{1},y_{1}) ~and~ (x_{2},y_{2})\]