Three points

Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out:
(a) whether the triangle KLM is right
b) calculate the length of the line to the k side
c) write the coordinates of the vector LM
d) write the directional form of the KM side
e) write the directional form of the axis of the KM side

Result

p =  1
t =  4.4721
x =  4
y =  -8
s = (Correct answer is: s=y=-x-1) Wrong answer

Solution:

kx=3;ky=2 lx=1;ly=4 mx=3;my=4 k=(lxmx)2+(lymy)2=((1)3)2+(4(4))2=4 58.9443 l=(kxmx)2+(kymy)2=((3)3)2+(2(4))2=6 28.4853 m=(kxlx)2+(kyly)2=((3)(1))2+(24)2=2 22.8284  k>l>m k2=l2+m2=8.48532+2.82842=4 58.9443 k2=k LKM=90  p=1
t=k/2=8.9443/2=2 5=4.4721
x=mxlx=3(1)=4
y=myly=(4)4=8
f(x)=y=kx+q k=kymykxmx=2(4)(3)3=1 q=myk mx=(4)(1) 3=1  s=y=x1



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Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Do you want to convert length units?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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