SOLUTION: Use the distance formula and the converse of the Pathagorean [sic] Theorem to determine whether the points are vertices of a right triangls. (please show all work) 1.(1.-4),(5,6

Question 1033888: Use the distance formula and the converse of the Pathagorean [sic] Theorem to determine whether the points are vertices of a right triangls. (please show all work)
1.(1.-4),(5,6),(-2,3)
2.(-2,4),(5,3),(0,-1)
3.(2,1),(6,-3),(-5,1)
THANKS
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Use the distance formula and the converse of the Pathagorean Theorem to determine whether the points are vertices of a right triangls.(please show all work)
1.(1.-4),(5,6),(-2,3)
2.(-2,4),(5,3),(0,-1)
3.(2,1),(6,-3),(-5,1)
----------------
Label the points
L(1,-4), M(5,6), N(-2,3)
--
Find the length of LM, LN and MN
If the square of the longest = the sum of the squares of the other 2, it's a right triangle. (Unless they're colinear).
-----
LM^2 = diffy^2 + diffx^2 = 4^2 + 10^2 = 116
LN^2 = 3^2 + 7^2 = 58
MN^2 = 7^2 + 9^2 = 130
---
130 <> 110 + 58 --> not a right triangle.
==============
Do the others the same way.

RELATED QUESTIONS
The converse of the Pythagorean theorem is also a true statement: If the sum of the... (answered by Edwin McCravy)

Use the distance formula to determine whether the given points are collinear. (0,1),... (answered by jim_thompson5910)

The question says: Use Pathagorean Theorem to find the distance between each pair of... (answered by stanbon,MathTherapy)

State the postulate or theorem you would use, to prove that lines m and n are parallel. (answered by RAY100)

Using the distance formula and the Pythagorean theorem, determine whether the following... (answered by Theo)

Tenille and Jana were asked to determine if a triangle on a coordinate plane is a right... (answered by ikleyn)

what is the proof for the collary to theorem 4.7 (converse of the base angles... (answered by Edwin McCravy)

Show that the points A = (-2,0), B = (-4,4), and C = (8,5) are the vertices of a right... (answered by josgarithmetic,math_tutor2020)

Show that the points(5,7), (3,9) and (6,8) are the vertices of a right triangle.... (answered by venugopalramana)