SOLUTION: show in a new way that the points (-1 -2), (5 4), (-3 0) are the vertices of a right triangle

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Question 1045545: show in a new way that the points (-1 -2), (5 4), (-3 0) are the vertices of a right triangle
Found 3 solutions by ikleyn, blaser411, robertb:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
1.  Calculate the length of each of the tree sides of the triangle, using the formula for the distance between the points in a coordinate plane.


2.  Then check that the square of the longest of the three sides is the sum
    of squares of the two other sides (Pythagorean equality).

I don't know what the words "in a new way" mean in this context.


Answer by blaser411(1)   (Show Source): You can put this solution on YOUR website!

Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
A vector associated with the points (-1,-2) and (5,4) is < 5--1, 4--2 > = < 6, 6 >.
A vector associated with the points (-1,-2) and (-3,0) is < -3--1,0--2 > = < -2,2 >.
Two vectors are perpendicular (or orthogonal) if their dot product is 0,
< 6,6 >*<-2,2 > = -12 + 12 = 0.
This, however, is not a new way, just a little level higher.
Another way of showing this perpendicularity, but still not a "new" way, just a level lower, is
getting the slope of the line passing through (-1,-2) and
(5,4) and comparing this with the slope of the line passing through (-1,-2)
and (-3,0).
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