Determine whether the three points are the vertices of a right...

Question

Determine whether the three points are the vertices of a right triangle. See Example 3.

$(- 2, - 5), (1, 7), (3, 15)$

Accepted Answer

Identify if the three points giving can form a right triangle where we have point A point B. And point C. Now to determine this we're gonna use the distance formula which means the distance between two points is given by the difference in x is squared plus the difference is y squared all under the square root. Let's say you want the distance between points A. And B. First we'll have the square root X two minus x one so X two negative one. Y two X 1 is -3. Then we do Y two just two minus negative eight. Quick. Now we can compute the square root by simplifying we get the square root four plus 100 which is a square of 104. Let's check B. C. Next that is the square root of - state of one square plus 17 -2 Squared. She is this square root of nine plus 25 which is the square root of 2 34. Finally we'll do a c square root two minus negative three square Plus 17 -20 sq It's square root 25. A 6 25. Where of 6 50. Now to determine if these make a red triangle, we want to see if the square of the longest length is equal to the sum of squares of the shorter lengths. In other words, our longest length we notice is square to 650. I wanna see if this squared is equal to the sum of our other links squared one of 4 squared and Square root 34 squared. When we square radical like this, it's just going to go away, which means we get 1 to 4 left. Same here to 34 the right side. We get 6 50 add these together, we get 3 37 equals 6 50 which in this case is not true since they don't equal each other. We will then say no. We cannot make a rectangle from these three points. Okay, hope to help you solve the problem. Thank you for watching. Goodbye.

Determine whether the three points are the vertices of a right triangle. See Example 3.
$(- 2, - 5), (1, 7), (3, 15)$

Key Concepts

Distance Formula

Pythagorean Theorem

Coordinate Geometry and Triangle Classification

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