Three points

Three points, K (-3; 2), L (-1; 4), and 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

Correct answer:

p =  1
t =  4.4721
x =  4
y =  -8
s : s=y=-x-1

Step-by-step explanation:

kx​=−3;ky​=2 lx​=−1;ly​=4 mx​=3;my​=−4 k=(lx​−mx​)2+(ly​−my​)2​=((−1)−3)2+(4−(−4))2​=4 5​≐8.9443 l=(kx​−mx​)2+(ky​−my​)2​=((−3)−3)2+(2−(−4))2​=6 2​≐8.4853 m=(kx​−lx​)2+(ky​−ly​)2​=((−3)−(−1))2+(2−4)2​=2 2​≐2.8284  k>l>m k2​=l2+m2​=8.48532+2.82842​=4 5​≐8.9443 k2​=k ∠LKM = 90°  p=1
t=k/2=8.9443/2=2 5​=4.4721
x=mx​−lx​=3−(−1)=4
y=my​−ly​=(−4)−4=−8
f(x)=y = kx​+q k=kx​−mx​ky​−my​​=(−3)−32−(−4)​=−1 q=my​−k⋅ mx​=(−4)−(−1)⋅ 3=−1  s:s=y=−x−1

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
The line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
Do you want to convert length units?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: