Question

Please help me it is due soon, please no links

Answer 1

The length of the three sides
`5, √(58) , √(65)`

The triangle is not a right triangle

Explanation:

A = (3, 2) , B = ( 6, 9) , C = (10, 6)

Find the lengths using distance formula.

`distance = √((x_2 -x_1)^2 + (y_2 - y_1)^2)`

`AB = √((6-3)^2 + (9-2)^2) = √(9 + 49 ) = √(58)`

`BC = √((10-6)^2 + (6-9)^2) = √(16 + 9) = √(25) = 5`

`AC = √((3-10)^2+(2-6)^2) = √(49 + 16) = √(65)`

Using Pythagoras theorem :

`(Longer \ side)^2 = sum \ of \ square \ of \ two \ other \ sides`

Longest side is AC . So we will check if it satisfies Pythagoras theorem :

`√(65) = √(58) + 5^2\\65 = 58 + 25\\`

65 ≠ 58 + 25

So the sides does not satisfy Pythagoras theorem. Hence the triangle is not a right triangle.