Question

On a coordinate plane, a triangle is shown. It has points (1, 4), (5, negative 2), and (negative 3, negative 2). Mary thinks the triangle is equilateral. How would you support or dispute her conjecture? Calculate the slope of all three sides, and check whether the slopes are equal. Calculate the slope of all three sides, and check whether any slopes are reciprocals. Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent. Use the distance formula to calculate the length of all three sides, and check whether any two sides are congruent.

Answer 1

Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.

Explanation:

Equilateral triangle has 3 sides and 3 internal angles congruent.

Slopes won't help as internal angles are 60 deg. Distance of 2 sides won't help as it will mean the triangle is isosceles.

So the correct option is:

Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.

Answer 2

• Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.

Explanation:

Equilateral triangle has 3 sides and 3 internal angles congruent.

Slopes won't help as internal angles are 60 deg. Distance of 2 sides won't help as it will mean the triangle is isosceles.

So the correct option is:

• Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.