Triangle abc has vertices a(0,4), b(1,2), and c(4,6). determine whether abc is a right triangle. explain

For it to be a right triangle, it must have a right angle.
Right angles are formed by perpendicuar lines.
If we find that two of these lines are perpendicular, we will know it is a rt. triangle.

Perpendicular lines have slopes which are opposite reciprocals (like 3 and -1/3)

To find the slope between two points, use the formula .

For line AB:


For line AC:


For line BC:


-2 and 1/2 are opposite reciprocals, so this must be a right triangle.

Another way to do this would be to use the distance formula to find the three side lengths and see if the Pythagorean Theorem applies.