Determine whether a triangle with the given vertices is a scalene, isosceles, or equilateral triangle. Check all that apply.

9514 1404 393

  (a) isosceles

  (b), (c) scalene

Step-by-step explanation:

The lengths of the sides can be found from the distance formula:

  d = √((x2 -x1)^2 +(y2 -y1)^2)

Here, there are 9 lengths to be computed, so it is useful to let a spreadsheet or graphing calculator do it.

We find triangle (a) has two sides the same length, so it is isosceles.

The other two triangles have three different side lengths, so they are scalene.

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Additional comment

It is impossible to specify an equilateral triangle using rational coordinates.