Question

Which classification describes AMNO with vertices M(2, -3), N(3, 1), and
0(-3, 1)?

Answer 1

Option D

Explanation:

32). Given vertices of the triangle are M(2, -3), N(3, 1) and O(-3. 1).

Distance between two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by the expression,

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

Distance between M(2, -3) and N(3, 1) will be,

MN =
`√((3-2)^2+(1+3)^2)`

=
`√(1+16)`

=
`√(17)`

Distance between M(2, -3) and O(-3, 1),

MO =
`√((2+3)^2+(-3-1)^2)`

=
`√(25+16)`

=
`√(41)`

Distance between N(3, 1) and O(-3, 1),

NO =
`√((3+3)^2+(1-1)^2)`

= 6

Condition for right triangle,

c² = a² + b² [Here c is the longest side of the triangle]

By this property,

MO² = MN² + NO²

`(√(41))^2=(√(17))^2+6^2`

41 = 17 + 36

41 = 51

False.

Therefore, given triangle is not a right triangle.

Since, length of all sides are not equal, given triangle will be a scalene triangle.

Option D is the correct option.