Question

The triangle formed by the points A(2, 0), B(1, 3) and C(-1, -1) is a/an triangle.

• A. equilateral
• B. isosceles
• C. scalene

Answer 1

The correct option is B isosceles


Distance from A to B

$AB=\sqrt{(1-2{)}^2+(3-0{)}^2}$
$=\sqrt{(-1{)}^2+(3{)}^2}$
$=\sqrt{1+9}$
$=\sqrt{10}units$

Distance from B to C

$BC=\sqrt{(-1-1{)}^2+(-1-3{)}^2}$
$=\sqrt{(-2{)}^2+(-4{)}^2}$
$=\sqrt{4+16}$
$=\sqrt{20}units$

Distance from C to A

$CA=\sqrt{(2-(-1){)}^2+(0-(-1){)}^2}$
$=\sqrt{(2+1{)}^2+(0+1{)}^2}$
$=\sqrt{(3{)}^2+(1{)}^2}$
$=\sqrt{9+1}$
$=\sqrt{10}units$

Since, the length of two sides (AB and CA) of the triangle ABC are equal, the given points form an isosceles triangle.