Can anyone help me in this. My answer is coming wrong

Question

Determine if the triangle with the given vertices is a right triangle, isosceles triangle, neither, or both.

(Recall that a right triangle satisfies the Pythagorean theorem and an isosceles triangle has at least two sides of equal length.)

(1, 1), (1,3), and (5, 2)

The triangle is right, not isosceles.

The triangle is right, and it may be isosceles.

O The triangle is isosceles and right.

O The triangle is isosceles, not right.

O The triangle is neither isosceles nor right.

Answer 1

Recall the distance formula btn two points (x1, y1), (x2, y2) - d=√(x₂ – x₁)² + (y₂ – y₁)²)

Apply this formula to each pair of coordinates - (1,1), (1,3), and (5,2)

(1,1), (1,3) - d = √(1-1)²+(3-1)² = 2

(1,1), (5,2) - d = √(5-1)²+(2-1)² = √17

(1,3), (5,2) - d = √(5-1)²+(2-3)² = √17

Since two of the sides have equal lengths, the triangle is isosceles.

The side lengths do not satisfy the Pythagorean theorem, so the triangle is not right.

Thus, the correct answer is - the triangle is isosceles, not right.

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