Question

Do the segments connecting points A, B, and C form a right triangle? Show work that leads to your answer. Round to the nearest tenths place if necessary.

A= -2,2
B=6,2
C=0,6

Answer 1

Explanation:

we need to calculate the distances between the points as the side lengths of the triangle.

these side lengths must satisfy the Pythagoras principle :

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle) and the longest of the 3 sides, a and b being the legs.

the distance between 2 points is again calculated via Pythagoras, as the coordinate differences (= the legs) with the distance as Hypotenuse create right-angled triangles.

this is then caked the distance formula, but it is all Pythagoras again.

AB² = (xB - xA)² + (yB - yA)² = (6 - -2)² + (2 - 2)² =

= 8² + 0² = 8²

AB = 8

AC² = (0 - -2)² + (6 - 2)² = 2² + 4² = 4 + 16 = 20

AC = sqrt(20)

BC² = (0 - 6)² + (6 - 2)² = (-6)² + 4² = 36 + 16 = 52

BC = sqrt(52)

as sqrt(20) is a little bit more than 4, and sqrt(52) is a little bit more than 7, 8 is the longest side and Hypotenuse.

if this is a right-angled triangle, then

8² = sqrt(20)² + sqrt(52)²

must be true.

but

64 = 20 + 52 = 72

is wrong.

so, the segments do not form a right-angled triangle.