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. (-4,3),(2,5),(-1,-6)

Accepted Answer

Identify three points giving can form a right triangle. So we have our three points here. I'll name those A. B and C. To solve this, we first want to find the distance between every one of these three points I wrote the distance scoring go down which is the square root of our x values squared plus our y values squared. The difference between those values some let's say you want the distance between A and B. First you take the square root of -9 -8 before squared plus 5 -9 Squared which is a square of 25 plus 16 which is the square of will do the same for bc square rip of -1 - of nine sq plus negative five minus five. It's quick. That is a square of 64 plus 100 which is square root of one, Finally we want a C. Should give us the square root -1 might say the four squared plus 95 -9 Squared. Simplifying this, we get the square root of nine Plus 1 which is the square root of 205. Now, it's a term of these former red triangle. You want to see if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides. In other words, our longest side is squared. To effect, we want to see if this squared is equal to the sum of the other side squared squared of 41 squared plus square root of 1, 64 squared what A square root race to the second power just removes the square root, so we will get 41 Plus 1 64 is equal to 205. They both equal the same number, which means that we can form a right channel between these points, so yes, we can. Okay? I hope to help you solve the problem. Thank you for watching. Goodbye.

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Determine whether the three points are the vertices of a right triangle. See Example 3. (-4,3),(2,5),(-1,-6)

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