SOLUTION: As isosceles triangle is a triangle that has two equal sides. Find AB, BC and AC. Determine if the triangle is isoseles or not based on the lengths of the three sides. Show all you

Algebra ->  Triangles -> SOLUTION: As isosceles triangle is a triangle that has two equal sides. Find AB, BC and AC. Determine if the triangle is isoseles or not based on the lengths of the three sides. Show all you      Log On


   

Question 48568: As isosceles triangle is a triangle that has two equal sides. Find AB, BC and AC. Determine if the triangle is isoseles or not based on the lengths of the three sides. Show all your work.
A(1,1) B(1,5) C(5,3)
I know that it is isosceles but i dont know how to find the length of the sides?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can use the distance formula to find the distance between the pairs of given points:
A(1, 1), B(1, 5), C(5, 3)
Distance formula is: d+=+sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29 where the x1 and y1 are the x- and y-coordinates of one of the pair of points and the x2 and y2 are the x- and y-coordinates of the second point.
Distance between point A(1, 1) = (x1, y1) and B(1, 5) = (x2, y2) is found as follows:
AB+=+sqrt%28%281-1%29%5E2%2B%285-1%29%5E2%29
AB+=+sqrt%284%5E2%29
AB+=+4
Distance between point B(1, 5) and C(5, 3) is found by:
BC+=+sqrt%28%285-1%29%5E2%2B%283-5%29%5E2%29
BC+=+sqrt%284%5E2%2B%28-2%29%5E2%29
BC+=+sqrt%2816%2B4%29
BC+=+sqrt%2820%29
BC+=+2sqrt%285%29
The distance between point A(1, 1) and C(5, 3) is found by:
AC+=+sqrt%28%285-1%29%5E2%2B%283-1%29%5E2%29
AC+=+sqrt%284%5E2%2B2%5E2%29
AC+=+sqrt%2820%29
AC+=+2sqrt%285%29
As you can see, sides BC and AC are of equal length, therefore the triangle is isosceles.