Question 446465
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The vertices of the triangle are A(6,1), B(6,7) and C(10,7) show that the triangle is right angled and find it's sides?
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            It is so simple . . . - much simpler than you think.



<pre>
The side AB is vertical line x = 6,  since points A and B have the same x-coordinate 6.

The side BC is horizontal line y = 7, since points B and C have the same y-coordinate 7.



        Therefore, triangle ABC is a right-angled triangle.



The length of side AB is the difference y-coordinates points A and B  |7-1| = 6 units.

The length of side BC is the difference x-coordinates points B and C  |10-6| = 4 units.

The hypotenuse  AC has the length  {{{sqrt(6^2+4^2)}}} = {{{sqrt(36+16)}}} = {{{sqrt(52)}}} units.
</pre>

At this point, the problem is solved completely: all questions are answered.


You do not need to make complicated reasoning or complicated calculations, as @mananth does.



This problem teaches you to retrieve out geometric information from coordinates
of given points in coordinate plane.