Question

Name the type of triangle formed by the points A(-5,6), B(-4,-2) and C(7,5).

• A. Right-angled triangle
• B. Isosceles triangle
• C. Scalene triangle
• D. Equilateral triangle

Answer 1

The correct option is C

Scalene triangle

To find the type of triangle, first, we determine the length of all the three sides and see if the condition of the triangle is satisfied by these sides.
Now, using distance formula between two points,
$AB=\sqrt{(-4+5{)}^2+(-2-6{)}^2}=\sqrt{(1{)}^2+(-8{)}^2}=\sqrt{1+64}=\sqrt{65}[\because d=\sqrt{(x_2-x_1)+(y_2-y_1{)}^2}]BC=\sqrt{(7+4{)}^2+(5+2{)}^2}=\sqrt{(11{)}^2+(7{)}^2}=\sqrt{121+49}=\sqrt{170}AndCA=\sqrt{(-5-7{)}^2+(6-5{)}^2}=\sqrt{(-12{)}^2+(1{)}^2}\sqrt{144+1}=\sqrt{145}$
We see that, $AB\ne BC\ne CA$
And $\Delta ABC$ does not satisfy Pythagoras theorem
Hence, the required triangle is scalene because all sides are of different length.