Question

1. Find the area of the triangle whose vertices are
(2, 3) (-1,0), (2, -4)​

Answer 1

The area of the triangle is "10. 5 square units".

Step-by-step explanation:

Let the three vertices of triangle are

A(2, 3),  B(-1,0) and  C(2, -4)​.

Here,$x_1 = 2, y_1 = 2, x_2 = - 1, y_2 = 0$and $x_3 = 2, y_3 = - 4.$

∴ Area of triangle ABC

= $\dfrac{1}{2}$ ·${x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}$

= $\dfrac{1}{2}$ ·${2(0 + 4) - 1(- 4 - 3) + 2(3 - 0)}$

= $\dfrac{1}{2}$ ·( 8 + 7 + 6) Square units

= $\dfrac{21}{2}$  square units

= 10. 5 square units

Hence, the area of the triangle is "10. 5 square units".