Question

A triangle has vertices A(-1,3,4) , B(3,-1,1,) and C(5,1,1). Prove that it is right-angled?
And how do you determine the fourth vertex needed to complete a triangle?
Please help.

Answer 1

> Prove that it is right-angled?

Do you know how to use the Pythagorean theorem?

> And how do you determine the fourth vertex needed to complete a triangle?
Please help.

Triangles have only three vertices... not four.

Answer 2

can you draw the triangle for me please

Answer 3

i am confused with three vertex and don't know how to draw it.

Answer 4

The triangle is in 3d space. It's hard to draw accurately without a computer.

Question -- do you know how to use the Pythagorean Theorem?

Answer 5

yes

Answer 6

Ok, so the trick to this problem is the following:

Find the lengths of

AB
BC
AC

using the Pythagorean theorem.

Then see if the identity holds: (small)^2 + (small)^2 = (large)^2

Answer 7

what do you mean by small^2?

Answer 8

you could also do this problem by finding slopes between points. If any two slopes are negative inverses, then the lines are perpendicular, and the triangle would be a right triangle.

Answer 9

how do if ind the slope then? with three vertix

Answer 10

just pick any two points at a time, find the slope as (y2 - y1) / (x2 - x1)

If you get a slope of, for example, 2, for one pair of points, and a slope of -(1/2) for another pair of points, the lines between those pairs are perpendicular.

Answer 11

you may have to try all three pairs... AB, BC, and AC.

You could also do it with the distance formula method that was talked about up above... I was just suggesting the slope approach as an alternative.

Answer 12

i don't get how to do the formula method though, can you explain?

Answer 13

@Xetrevon You will find three lengths. If they are the lengths of a right triangle, then the sum of the squares of the smaller lengths will equal the square of the largest length.

Answer 14

do i just add the vectix then? Like A+B to find the length, How would i be able to used the Pythagorean theorem to do that with three numbers?

Answer 15

Here is a visual of finding distance between 2 points in 3d http://quiz.uprm.edu/visual3d/manual/coor_sys/dist_two_points.html
and lots of examples here
http://tutorial.math.lamar.edu/Classes/CalcIII/3DCoords.aspx

Answer 16

Thx for the help

Answer 17

sorry for the diversion about slope... bad eyes or bad browser scrolling or something, but I didn't see earlier that the points were in 3d.

In 3d, distance formula as @mathteacher1729 discussed would be much more appropriate.

Answer 18

what is the fourth vector needed to complete a rectangle?