Question

Is TVS scalene, isosceles, or equilateral? The vertices are T(1,1), V(9,2), and S(5,8).

- scalene
- equilateral
- cannot be determined
- isoceles

Answer 1

the triangle is Isoceles

Answer 2

(D) isosceles

Explanation:

The vertices of the triangle TVS is given as:

T(1,1), V(9,2), and S(5,8).

Now., TV=
`\sqrt{(2-1)^(2)+(9-1)^2}=√(1+64)=√(65)units`,

VS=
`\sqrt{(2-8)^(2)+(9-5)^2}=√(36+16)=√(52)units` and

ST=
`\sqrt{(1-8)^(2)+(1-5)^2}=√(49+16)=√(65)units`

Since, two sides of the given triangle TV and ST are equal, therefore, TVS is an isosceles triangle.

Since, in scalene triangle, all the three sides are unequal, but in this we have two equal sides, thus TVS is not a scalene triangle.

Moreover, In equilateral triangle, all the sides are equal, thus TVS is also not an equilateral triangle.