Question

Given below are the coordinates of the vertices of a triangle. Find the lengths of the sides of the triangle, then click to identify the triangle as scalene, isosceles, or equilateral.

R(1, 3), S(3, 1), T(5, 2)

Answer 1

Scalene

Explanation:

Hope this helps.

Answer 2

To find the length of the sides, we use the Pythagorean Theorem. First, let's look at the side RS. R is at (1,3), and S is at (3,1). Therefore, to find RS, we use the difference in height and length:
`a = \sqrt{ {b}^(2) + {c}^(2) } \\ a = \sqrt{ {(3 - 1)}^(2) + {(1 - 3)}^(2) } \\ a = \sqrt{ {(2)}^(2) + {( - 2)}^(2) } \\ a = √(4 + 4) \\ a = √(8)`
The length of side RS is square root 8.

Side ST is made from point S (3,1) and point T (5,2).

`a = \sqrt{ {(5 - 3)}^(2) + {(2 - 1)}^(2) } \\ a = \sqrt{ {(2)}^(2) + {(1)}^(2) } \\ a = √(4 + 1) \\ a = √(5)`
The length of side ST is root 5.

Side RT is between R (1,3) and T (5,2).

`a = \sqrt{ {(1 - 5)}^(2) + {(3 - 2)}^(2) } \\ a = \sqrt{ {( - 4)}^(2) + {(1)}^(2) } \\ a = √(16 + 1) \\ a = √(17)`
The side RT is root 17. The triangle is scalene, meaning it has three sides of different lengths.