Question

In Δabc, the coordinates of vertices a and b are a(1,2) and b(-3,-1). For each of the given coordinates of vertex c, is Δabc a right triangle?

1) right triangle
2) not a right triangle

Answer 1

To determine if triangle ABC is a right triangle, we can use the Pythagorean theorem.

Step-by-step explanation:

To determine if triangle ABC is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

Let's calculate the lengths of the sides using the given coordinates.

1. Calculate the length of side AB: AB = sqrt((x2-x1)^2 + (y2-y1)^2)
2. Calculate the length of side AC: AC = sqrt((x3-x1)^2 + (y3-y1)^2)
3. Calculate the length of side BC: BC = sqrt((x3-x2)^2 + (y3-y2)^2)

If AB^2 + AC^2 = BC^2 or AB^2 + BC^2 = AC^2 or AC^2 + BC^2 = AB^2, then the triangle is a right triangle. Otherwise, it's not a right triangle.