Question

Could the points (-4,3), (-1,1) and (1,3) form the vertices of a right triangle? Why or why not?

Answer 1

Why not plot these three points, draw the triangle in question, and then determine whether the triangle appears to be a right triangle or not (does it appear to have a 90 degree angle?).
A more sophisticated way to check whether or not this is a right triangle would be to use the Pythagorean Theorem. Find the lengths of the 3 sides of the triangle and determine whether the equation (longest side)^2 = (length of leg #1)^2 + (length of leg #2)^2 is true or false. If true, you've got a right triangle. If not, you don't.

Answer 2

I have plotted these points and I have tried using the Pyth. Therom however one of the side lengths keeps saying it is .67 however it is much larger but i am just confused so any help would help

Answer 3

another is to compare the slope of the lines that will include the legs of the right triangle, if they are perpendicular, their slope is negative reciprocal of the other, the measure of their intersecting angle is 90... as well as the coefficients A & B are reversed for perpendicular lines.... that is... if
line L1 is Ax + By + C = 0 with a slope m1...
line L2 is Bx + Ay + D = 0 with a slope m2 = -1/m1
these two lines, form the legs of the triangle...
the line L3 will intersect at a points given in this problem to form the longest side of the triangle called hypotenuse....
as @mathmale mentioned applying Pythagorean theorem or comparing the distances of points to satisfy the theorem will lead to verify whether the given vertices are for right triangle....

Answer 4

caroo8: are you familiar with finding the length of a straight line connecting two points? If so, find the length of each side of the triangle formed by the given points.
To give you something to compare: I've determined that the length of the line connecting (-4, 3) and (1, 3) is 5. My other two length results are Sqrt(13) and Sqrt(8).

Answer 5

The greatest of these lengths is 5. The lengths of the other two sides are given above.
Square 5; you'll get 25. Square Sqrt(13) and Sqrt(8). You'll get 13 and 8, respectively. Now use the Pythagorean Theorem to check whether or not the triangle is a right triangle: Does 25 = 13 + 8? No. So, what's your conclusion?