Question

F. Do the segments connecting the coordinates (-1,6), (4,2), and (7,6) form a right triangle? Show

work that leads to your answer.

Answer 1

No, these segments do not form a right triangle.

Explanation:

We need to calculate the distances between the points, taking 2 at a time:

From (-1, 6) to (4, 2), x increases by 5 and y decreases by 4. The distance between the two points, by the Pythagorean Theorem, is d = √(5² + 4²), or √41.

From (-1, 6) to (7, 6) x increases by 8 but y stays the same: 6. The distance between these two points is therefore 8.

Finally, from (4, 2) to (7, 6), x increases by 3 and y by 4, and so d = 5.

So now we have the 3 side lengths: √41, 8 and 5.

Squaring them, we get 41, 64 and 25. These do not satisfy the Pythagorean Theorem: 41 + 25 is not equal to 64.

No, these segments do not form a right triangle.