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

Question

Determine whether the three points are the vertices of a right triangle. See Example 3. (-4,1),(1,4),(-6,-1)

Accepted Answer

Identify if the three points giving can form a right triangle are three points are A. B and C. Now to do this will make use of the distance formula which gives us the distance between each of our points. This is formula is given by X two minus X one squared plus Y two minus y one square and all that under square root. Let's go and find this between A&B. 1st. This is between A and B. It's given by the square root X two. So we have negative 9 -8 of five squared plus 6 -8 sq She is a square 16 plus four which is the square of 20. We'll do the same for B. C. Now B C will be two minus negative nine squared Plus 7 -6 Squared. Is this square of 1 21 plus one which is the square root of 22. Finally we'll do a C. We have the square root F two - State of five squared Plus 7 -8 sq. Excuse us square 49 plus one with square 50. Now to determine if these make a red triangle, we want to see if the square of the longest side is equal to the sum of squares of the smaller side. So in other words, let's see what our longest side is. We'll see Along the side is squared of 1 22. We're gonna square that. Now we're going to see if the shorter sides. The some of those squares are equal to the square of 122 squared. Other words square of 20 squared plus squared of squared When we square radical like this, the radical just goes away. We just left foot 20. Same for the 50 50 and same for the We didn't end up with 70 is equal to 122. That is a false statement. Because it's the false statement. We can conclude that these three points do not form a right triangle. So you will say answer is B no. Okay. I 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. (-4,1),(1,4),(-6,-1)

Key Concepts

Distance Formula

Pythagorean Theorem

Collinearity

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