Question

If coordinates of the triangle are A(-2,4), B(2,4) and C(-2,1), then the triangle is ______________.

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

Answer 1

Answer: (B)

right angled triangle

In the given question, we need to find the shape of the polygon formed. By finding the length of the sides we will be able to find the property of the particular triangle. Distance between AB = $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
= $\sqrt{(2-(-2){)}^2+(4-4{)}^2}$
= $\sqrt{(4{)}^2+0}$
= 4 units
Distance between BC = $\sqrt{(x_2-x_3{)}^2+(y_2-y_3{)}^2}$
= $\sqrt{(2-(-2){)}^2+(4-1{)}^2}$
= 5 units
Distance between AC = $\sqrt{(x_3-x_1{)}^2+(y_3-y_1{)}^2}$
= $\sqrt{\left(\right(-2)-(-2){)}^2+(1-4{)}^2}$
= 3 units
Here,
$A{B}^2$ + $A{C}^2$ = $B{C}^2$
i.e. $4^2$ + $3^2$ = $5^2$
Therefore, it forms a right angled triangle.