Question

Graph the points. Decide whether they are vertices of a right triangle. $$(-2,2),(3,4),(4,2)$$

Short answer

After calculating the lengths of the sides, apply the Pythagorean theorem to determine if it’s a right triangle. The answer depends on whether or not the theorem holds true.

Step-by-step solution

Plot the Points on the Graph

Plot the given points \(-2,2\), \(3,4\), and \(4,2\) on the graph. Join these points to form a triangle.

Calculate the Lengths of the Sides of the Triangle

Calculate the lengths of the sides of the triangle using the formula for the distance between two points, which is \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Apply the Pythagorean theorem

Once the lengths are calculated, identify the longest side. Then apply the Pythagorean theorem to see if the square of the longest side is equal to the sum of the squares of the other two sides. If it is, then the triangle is a right triangle.