Determine whether or not the triangle with vertices a(1,2) , b(5,5) and c(-1,13) . Use graphical evidence to determine whether or not the triangle is a right triangle

Question

Determine whether or not the triangle with vertices a(1,2) , b(5,5)  and c(-1,13) . Use graphical evidence to determine whether or not the triangle is a right triangle

tkhunny · Answer

1) Are they collinear?  If not, they form a unique triangle.

wolf1728 · Answer

Anyway I made a graphic
It appears it is a right triangle.

tkhunny · Answer

"Appears"?  It is or it isn't.  Prove it!!

wolf1728 · Answer

That's what I was going to work on next.
Is there a quick test to determine a right angle OR do we have to determine lengths of each side?

tkhunny · Answer

Slopes of the intersecting lines?

wolf1728 · Answer

slope (5,5) (1,2)
= (5 -1)/(5 - 2)
= 4/3

slope (-1, 13) (5,5)
= (-1 -5) / (13 -5)
= -6 / 8 = -3/4

wolf1728 · Answer

slopes are 90° different therefore it is a right triangle.

tkhunny · Answer

Very nice.

wolf1728 · Answer

thanks :-)