# Vertices of a right triangle

Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.

Result

d =  0

#### Solution:

$x_{1}=2 \ \\ y_{1}=1 \ \\ x_{2}=4 \ \\ y_{2}=0 \ \\ x_{3}=5 \ \\ y_{3}=7 \ \\ \ \\ a=\sqrt{ (x_{1}-x_{2})^2+(y_{1}-y_{2})^2 }=\sqrt{ (2-4)^2+(1-0)^2 } \doteq \sqrt{ 5 } \doteq 2.2361 \ \\ \ \\ b=\sqrt{ (x_{1}-x_{3})^2+(y_{1}-y_{3})^2 }=\sqrt{ (2-5)^2+(1-7)^2 } \doteq 3 \ \sqrt{ 5 } \doteq 6.7082 \ \\ \ \\ c=\sqrt{ (x_{2}-x_{3})^2+(y_{2}-y_{3})^2 }=\sqrt{ (4-5)^2+(0-7)^2 } \doteq 5 \ \sqrt{ 2 } \doteq 7.0711 \ \\ \ \\ c^2=a^2 + b^2 ? \ \\ d=c^2-a^2-b^2=7.0711^2-2.2361^2-6.7082^2=-0=0$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
Be the first to comment!

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.
Do you want to convert length units?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

## Next similar math problems:

1. Vertices of RT
Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
2. Segment
Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
3. Spruce height
How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
4. Double ladder
The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
5. Three points
Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
6. Distance
Calculate distance between two points X[18; 19] and W[20; 3].
7. Distance
Wha is the distance between the origin and the point (18; 22)?
8. Triangle IRT
In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
9. Medians and sides
Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
10. Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
11. Right 24
Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
12. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
13. Double ladder
The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
14. Cable car
Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
15. Center
Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
16. Distance between 2 points
Find the distance between the points (7, -9), (-1, -9)
17. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?