Question

Is TRIANGLE TVS scalene, isosceles, or equilateral? The vertices are T(1, 1), V(4, 0), and S(3, 5).thank you ! :)

Answer 1

scalene triangle

EXPLANATION :

From the problem, the vertices of a triangle are :

T(1, 1), V(4, 0) and S(3, 5)

A triangle is scalene if the three sides are different from each other.

A triangle is isosceles if two sides are congruent.

A triangle is equilateral if three sides are congruent.

So we need to get the distances between two points and determine the type of triangle accordingly.

Using the distance formula :

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

The distances are :

`\begin{gathered} d_(TV)=√((4-1)^2+(0-1)^2)=√(10) \\ \\ d_(TS)=√((3-1)^2+(5-1)^2)=√(20) \\ \\ d_(VS)=√((3-4)^2+(5-0)^2)=√(26) \end{gathered}`

Since the distances are different from each other, the triangle is scalene