find the measures of each side of triangle abc with vertices a(-1,5), b(6,1), c(2,6) and classify the triangle.

Use you distance between 2 points formula, and find the 3 sides.

(2/3xy)(1/5xy)

87

To find the measures of each side of triangle ABC, you need to calculate the distances between its vertices. The distance formula between two points (x1, y1) and (x2, y2) is given by:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's calculate the measures of each side:

Side AB:
Distance_AB = √((6 - (-1))² + (1 - 5)²)
Distance_AB = √((7)² + (-4)²)
Distance_AB = √(49 + 16)
Distance_AB = √65

Side BC:
Distance_BC = √((2 - 6)² + (6 - 1)²)
Distance_BC = √((-4)² + (5)²)
Distance_BC = √(16 + 25)
Distance_BC = √41

Side AC:
Distance_AC = √((-1 - 2)² + (5 - 6)²)
Distance_AC = √((-3)² + (-1)²)
Distance_AC = √(9 + 1)
Distance_AC = √10

Therefore, the measures of each side of triangle ABC are:
Side AB = √65, Side BC = √41, and Side AC = √10.

To classify the triangle, we can use the lengths of the sides.

If all three sides are equal:
- If Side AB = Side BC = Side AC, the triangle is an equilateral triangle.

If two sides are equal:
- If Side AB = Side BC or Side BC = Side AC or Side AC = Side AB, the triangle is an isosceles triangle.

If no sides are equal:
- If Side AB ≠ Side BC ≠ Side AC, the triangle is a scalene triangle.

Now, using the measures of the sides:
Side AB = √65, Side BC = √41, and Side AC = √10.

Since none of the side lengths are equal, triangle ABC is classified as a scalene triangle.

thanks