# Vertices of RT

Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.

Result

x =  0

#### Solution:

$x_{1}=5 \ \\ y_{1}=0 \ \\ x_{2}=2 \ \\ y_{2}=1 \ \\ x_{3}=4 \ \\ y_{3}=7 \ \\ a=\sqrt{ (x_{1}-x_{2})^2+(y_{1}-y_{2})^2 }=\sqrt{ (5-2)^2+(0-1)^2 } \doteq \sqrt{ 10 } \doteq 3.1623 \ \\ b=\sqrt{ (x_{1}-x_{3})^2+(y_{1}-y_{3})^2 }=\sqrt{ (5-4)^2+(0-7)^2 } \doteq 5 \ \sqrt{ 2 } \doteq 7.0711 \ \\ c=\sqrt{ (x_{2}-x_{3})^2+(y_{2}-y_{3})^2 }=\sqrt{ (2-4)^2+(1-7)^2 } \doteq 2 \ \sqrt{ 10 } \doteq 6.3246 \ \\ x=b^2-(a^2+c^2)=7.0711^2-(3.1623^2+6.3246^2)=-0=0$

Try calculation via our triangle calculator.

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...):

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.
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. 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?
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?
3. Bisectors
As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
4. Triangle ABC
In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
5. Distance
Wha is the distance between the origin and the point (18; 22)?
6. 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.
7. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
8. Right angle
If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
9. 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.
10. Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
11. If the
If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .