SOLUTION: Show that the point (6,6),(2,3) and (4,7) are the vertices of a right angled triangle

Algebra.Com
Question 1009174: Show that the point (6,6),(2,3) and (4,7) are the vertices of a right angled triangle
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Let

P = (6,6)
Q = (2,3)
R = (4,7)

Find the slope of segment PQ to get


Find the slope of segment PR to get


Find the slope of segment QR to get


-------------------------------------------

Multiply the slopes of PR and QR to get

(slope of PR)*(slope of QR) = (-1/2)*(2) = -1

Since the product of the two slopes is -1, this means that segment PR and segment QR are perpendicular. We have a right angle form at where the segments meet (at point R)

So we definitely have a right triangle.
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
Show that the point (6,6), (2,3) and (4,7) are the vertices of a right angled triangle.
---------------------------------------------------------------------- 
Calculate the three segments in the coordinate plane that are sides of the triangle.

For example, one segment, connecting the points (6,6) and (2,3), is (6-2,6-3) = (4,3).
Its length is  =  = 5.

Two other segments are (2,-1) and (2,4).
Their lengths are  =  and  = .

Now notice that  = 25 and  +  = 5 + 20 = 25.

It is just enough to state that the triangle is right-angled.
The point (4,7) is the vertex of the right angle.


RELATED QUESTIONS

show that a triangle with vertices (5,-3) (2,-6) and (1,1) is a right angled triangle.... (answered by MathLover1)
Show that A(-1,-2),B(4,-2)and(4,3)are the vertices of a right-angled... (answered by benni1013)
show that the triangle whose vertices are A(3,6), B(-2,-4) and C(-5,2) is a right angled (answered by Alan3354)
Show in two ways that points 6 1 , 2 -3, and 4-5, are the vertices of a right triangle... (answered by josgarithmetic)
Show that the triangle whose vertices are A(4,3) B(6,-2) C(-11,3) is a right angled... (answered by KMST)
By using Slopes form, show that (3, 1), (6, 3) and (2, 9) are the vertices of a right... (answered by dolly)
The vertices of the triangle are A(6,1), B(6,7) and C(10,7) show that the triangle is... (answered by mananth)
If three angles of a triangle are in the ratio 3:7:10, show that triangle is right... (answered by Boreal,MathTherapy)
Hai Sir, please help me on this problem, i got stuck 1)Show that the points... (answered by ewatrrr)