SOLUTION: find the distance between each pair of points. Points L(-2,3),M(3,-2), and N(6,1) form a triangle. Show whether triangle LMN is a right triangle.

Algebra ->  Length-and-distance -> SOLUTION: find the distance between each pair of points. Points L(-2,3),M(3,-2), and N(6,1) form a triangle. Show whether triangle LMN is a right triangle.      Log On


   

Question 77689: find the distance between each pair of points.
Points L(-2,3),M(3,-2), and N(6,1) form a triangle. Show whether triangle LMN is a right triangle.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
find the distance between each pair of points.
Points L(-2,3),M(3,-2), and N(6,1) form a triangle. Show whether triangle LMN is a right triangle.
The formula for distance is highlight%28d=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29%29
Plotting the points will tell you that you need to find the distance of LM, MN, and LN.
For LM (x1,y1)=(-2,3) and (x2,y2)=(3,-2)
dLM=sqrt%28%283-%28-2%29%29%5E2%2B%28-2-3%29%5E2%29
dLM=sqrt%28%285%29%5E2%2B%28-5%29%5E2%29
dLM=sqrt%2825%2B25%29
dLM=sqrt%2850%29
For MN (x1,y1)=(3,-2) and (x2,y2)=(6,1)
dMN=sqrt%28%286-3%29%5E2%2B%281-%28-2%29%29%5E2%29
dMN=sqrt%28%283%29%5E2%2B%283%29%5E2%29
dMN=sqrt%289%2B9%29
dMN=sqrt%2818%29
For LN (x1,y1)=(-2,3) and (x2,y2)=(6,1)
dLN=sqrt%28%286-%28-2%29%29%5E2%2B%281-3%29%5E2%29
dLN=sqrt%28%288%29%5E2%2B%28-2%29%5E2%29
dLN=sqrt%2864%2B4%29
dLN=sqrt%2868%29
The pythagorean theorem says that the longest side squares is equal to the sum of the squares of the shortest sides. highlight%28c%5E2=a%5E2%2Bb%5E2%29
sqrt%2868%29%5E2=sqrt%2850%29%5E2%2Bsqrt%2818%29%5E2
68=50%2B18
68=68
Yes, this is a right triangle!
Happy Calculating!!!