Question

The triangle formed by joining the points (0,0), (2,2) and (4,6) will be a/an triangle.

• A. right-angled
• B. scalene
• C. equilateral

Answer 1

The correct option is B scalene

We know that, the distance between the points $(x_1,y_1)$ and $(x_2,y_2)$ is represented as:

$\text{Distance, d}=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

Now, let us represent the points (0,0), (2,2), and (3,-4) be as A, B, and C, respectively, and join them to find the length of the sides of the triangle formed.

$AB=\sqrt{(2-0{)}^2+(2-0{)}^2}$

$=\sqrt{(2{)}^2+(2{)}^2}$

$=\sqrt{4+4}=\sqrt{8}$

$=\sqrt{8}\text{units}$


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

$=\sqrt{(1{)}^2+(-6{)}^2}$

$=\sqrt{1+36}=\sqrt{50}$

$=\sqrt{37}\text{units}$


$AC=\sqrt{(3-0{)}^2+(-4-0{)}^2}$

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

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

$=5\text{units}$

All the three sides have three different lengths.

So, the triangle obtained is a scalene triangle.