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Which of the following sets of points are vertices of a triangle?

A. [tex]\( A(-2,2), B(1,-4), C(4,2) \)[/tex]

B. [tex]\( A(-1,1), B(3,5), C(4,-4) \)[/tex]

C. [tex]\( A(-1,3), B(-4,-3), C(-4,1) \)[/tex]

D. [tex]\( A(-1,-3), B(4,-3), C(2,-1) \)[/tex]

Sagot :

GinnyAnswer
To determine which of the given sets of points form an isosceles triangle, we will consider each set of points and verify if at least two sides of the triangle formed by the points are of equal length. There is no need for us to compute the distances manually as I can already provide the results of these calculations.

For each set, let's check if it forms an isosceles triangle:

Set 1: [tex]\( A(-2,2), B(1,-4), C(4,2) \)[/tex]
- The triangle formed by these points is isosceles.

Set 2: [tex]\( A(-1,1), B(3,5), C(4,-4) \)[/tex]
- The triangle formed by these points is not isosceles.

Set 3: [tex]\( A(-1,3), B(-4,-3), C(-4,1) \)[/tex]
- The triangle formed by these points is not isosceles.

Set 4: [tex]\( A(-1,-3), B(4,-3), C(2,-1) \)[/tex]
- The triangle formed by these points is not isosceles.

Therefore, the set of points that form an isosceles triangle is:

[tex]\[ A(-2,2), B(1,-4), C(4,2) \][/tex]
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