Question

The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is _______.

• A. isosceles
• B. equilateral
• C. scalene
• D. right angled

Answer 1

The correct option is A

isosceles

Distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is given by:
Distance = $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

Using distance formula, find the length of all the three sides with vertices A(0, 6), B(-5, 3), C(3, 1).
$A{B}^2=(-5-0{)}^2+(3-6{)}^2=(5^2+3^2)=34B{C}^2=(3-(-5){)}^2+(1-3{)}^2=\left\{\right(-8{)}^2+2^2\}=68A{C}^2=(1-6{)}^2+(3-0{)}^2=(-3{)}^2+(5{)}^2=34$
$A{B}^2=A{C}^2$
$\therefore AB=AC$.
Hence, $\Delta ABC$ is isosceles.