Question

Determine whether this is a right triangle

vertices: G(1, -1) H(5, 0) and J(3, 8)

Should I use distance formula to find the sides and use Pythagorean theorem to prove it? Or is there another method?

Thanks.

Answer 1

There are other methods (such as computing and comparing the slopes of the three lines) but I like your way.

GH^2 = 17
HJ^2 = 68
GJ^2 = 85
Looks like the Pythagorean theorem works. GJ is the hypotenuse.

Answer 2

The easiest way is to use the distance formula for points in the (x,y) form.

Use the formula 3 times.

You have triangle GHJ.

Use the formula from point:

G to H

H to J

G to J

Only then will you be able to tell if triangle GHJ is a right triangle or not.

Answer 3

given vertices of triangle G(1,-1),

H(5,0),J(3,8)
first find distance between G to H
i.e root of 5-1 whole square+root of 0-(-1) whole square
similarly find from H to J &Jto G
apply right angle theorm

Answer 4

[AI-generated answer — Explain Bot]

To determine whether a triangle is a right triangle, you can indeed use the distance formula and the Pythagorean theorem. Here's how you can approach it:

1. Use the distance formula to find the lengths of the three sides of the triangle. The distance formula between two points (x1, y1) and (x2, y2) is given by:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

2. Find the lengths of the three sides GH, GJ, and HJ using the distance formula.

GH = sqrt((5 - 1)^2 + (0 - (-1))^2)
GJ = sqrt((3 - 1)^2 + (8 - (-1))^2)
HJ = sqrt((5 - 3)^2 + (0 - 8)^2)

3. Now, use the Pythagorean theorem to determine whether the triangle is a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

If GH^2 = GJ^2 + HJ^2 or GJ^2 = GH^2 + HJ^2 or HJ^2 = GH^2 + GJ^2, then the triangle is a right triangle. If none of these equalities hold, the triangle is not a right triangle.

By following these steps, you can determine whether the triangle with vertices G(1, -1), H(5, 0), and J(3, 8) is a right triangle.