Question

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

Answer 1

Answer:

Option D

Step-by-step 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 = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

MN = $\sqrt{(3-2)^2+(1+3)^2}$

      = $\sqrt{1+16}$

      = $\sqrt{17}$

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

MO = $\sqrt{(2+3)^2+(-3-1)^2}$

      = $\sqrt{25+16}$

      = $\sqrt{41}$

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

NO = $\sqrt{(3+3)^2+(1-1)^2}$

      = 6

Condition for right triangle,

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

By this property,

MO² = MN² + NO²

$(\sqrt{41})^2=(\sqrt{17})^2+6^2$

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.