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

Is TRIANGLE TVS Scalene Isosceles Or Equilateral The Vertices Are T1 1 V4 0 And S3 5thank You class=

Sagot :

ANSWER :

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 :

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The distances are :

[tex]\begin{gathered} d_{TV}=\sqrt{(4-1)^2+(0-1)^2}=\sqrt{10} \\ \\ d_{TS}=\sqrt{(3-1)^2+(5-1)^2}=\sqrt{20} \\ \\ d_{VS}=\sqrt{(3-4)^2+(5-0)^2}=\sqrt{26} \end{gathered}[/tex]

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

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