Show that the points are vertices of a right triangle.
Where Points A(-1,1) B (3,3) and A(-1,1) C (1,-3) are the sides of a Right Triangle and Points B (3,3) C(1,-3) is the Base.
Given, d = sqrt (x[2] - x[1])^2 + y[2] -y[1]^2 then
sqrt [3 - (-1)]^2 + (3 -1)^2
sqrt (3 + 1)^2 + 2^2
sqrt 4^2 + 2^2
sqrt 16 + 4
sqrt 20 and
sqrt [1 - (-1)]^2 + (-3 - 1)^2
sqrt 2^2 + -4^2
sqrt 4 + 16
sqrt 20
sqrt (1 - 3)^2 + (-3 - 3)^2
sqrt -2^2 + -6^2
sqrt 4 +36
sqrt 40
so,
sqrt20^2 + sqrt20^2 = 20 +20 = 40
sqrt40^2 = 40
so these vertices are angles of a right triangle.
Please confirm if correct
Where Points A(-1,1) B (3,3) and A(-1,1) C (1,-3) are the sides of a Right Triangle and Points B (3,3) C(1,-3) is the Base.
Given, d = sqrt (x[2] - x[1])^2 + y[2] -y[1]^2 then
sqrt [3 - (-1)]^2 + (3 -1)^2
sqrt (3 + 1)^2 + 2^2
sqrt 4^2 + 2^2
sqrt 16 + 4
sqrt 20 and
sqrt [1 - (-1)]^2 + (-3 - 1)^2
sqrt 2^2 + -4^2
sqrt 4 + 16
sqrt 20
sqrt (1 - 3)^2 + (-3 - 3)^2
sqrt -2^2 + -6^2
sqrt 4 +36
sqrt 40
so,
sqrt20^2 + sqrt20^2 = 20 +20 = 40
sqrt40^2 = 40
so these vertices are angles of a right triangle.
Please confirm if correct