Question

What kind of a triangle is formed by the points (1, 1), (-2, -3) and (-8, -11) ?

• A. Right Angled Triangle
• B. Scalene Triangle
• C. Equilateral Triangle
• D. None of These

Answer 1

The correct option is B Scalene Triangle

Let the points (1, 1), (-2, -3) and (-8, -11) be represented by A, B and C respectively.

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

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

$AB=\sqrt{(3{)}^2+(4{)}^2}$

$AB=\sqrt{9+16}=\sqrt{25}$

AB = 5

$BC=\sqrt{(-2+8{)}^2+(-3+11{)}^2}$

$BC=\sqrt{(6{)}^2+(8{)}^2}$

$BC=\sqrt{36+64}=\sqrt{100}$

BC = 10

$AC=\sqrt{(1+8{)}^2+(1+11{)}^2}$

$AC=\sqrt{(9{)}^2+(12{)}^2}$

$AC=\sqrt{81+144}=\sqrt{225}$

AC = 15

Now, AB + BC = 5 + 10 = 15

Thus, AB + BC = AC

Therefore, the points (1, 1), (-2, -3) and (-8, -11) are collinear.

Hence, option d is correct.