Question

determine if the triangle with the following vertices is a right triangle. A(-3, 5), B(1, 4), and C(-1, 0). then tell if it is a right triangle or not and how you came to that conclusion

Answer 1

To determine if the triangle with the given vertices is a right triangle, we can use the Pythagorean theorem. Calculating the lengths of the sides and checking if the equation holds will help us come to a conclusion.

Step-by-step explanation:

To determine if the triangle with the vertices A(-3, 5), B(1, 4), and C(-1, 0) is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, we need to calculate the lengths of the three sides of the triangle and check if the equation holds.

Using the distance formula, we can calculate the lengths of the sides AB, BC, and AC:

AB = sqrt((1 - (-3))^2 + (4 - 5)^2) = 4.12

BC = sqrt((-1 - 1)^2 + (0 - 4)^2) = 4.47

AC = sqrt((-1 - (-3))^2 + (0 - 5)^2) = 5.39

Next, we check if the Pythagorean theorem holds:

AB^2 + BC^2 = AC^2

4.12^2 + 4.47^2 = 5.39^2

16.97 + 19.99 ≈ 29.09

Since the equation does not hold, the triangle with vertices A(-3, 5), B(1, 4), and C(-1, 0) is not a right triangle.

Answer 2

Yes, it is a right triangle; because, when you graph it on a graph paper, you can tell that it is a right triangle also you can use the Pythagorean Theorem to solve for. Pythagorean Theorem= a^2 +b^2 = c^2.