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 [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the expression,
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between M(2, -3) and N(3, 1) will be,
MN = [tex]\sqrt{(3-2)^2+(1+3)^2}[/tex]
= [tex]\sqrt{1+16}[/tex]
= [tex]\sqrt{17}[/tex]
Distance between M(2, -3) and O(-3, 1),
MO = [tex]\sqrt{(2+3)^2+(-3-1)^2}[/tex]
= [tex]\sqrt{25+16}[/tex]
= [tex]\sqrt{41}[/tex]
Distance between N(3, 1) and O(-3, 1),
NO = [tex]\sqrt{(3+3)^2+(1-1)^2}[/tex]
= 6
Condition for right triangle,
c² = a² + b² [Here c is the longest side of the triangle]
By this property,
MO² = MN² + NO²
[tex](\sqrt{41})^2=(\sqrt{17})^2+6^2[/tex]
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.
