Question

the area of the quadrilateral formed by the points( 1, 2) (2, - 3) (-2, 4) (0, 5)​

Answer 1

The area of the quadrilateral formed by the points( 1, 2), (2, - 3), (-2, 4) and (0,5)​ = 7.5 square units

Step-by-step explanation:

The given four points of the quadrilateral are (1, 2), (2, - 3), (- 2, 4) and (0, 5)​.

To find, the area of the quadrilateral formed by the points( 1, 2) (2, - 3) (-2, 4) (0, 5)​ = ?

We know that,

The area of the quadrilateral

= $\dfrac{1}{2} [x_{1} (y_{2} -y_{3})+x_{2} (y_{3} -y_{4})+x_{3} (y_{4} -y_{1})+x_{4} (y_{1} -y_{2})]$

∴ The area of the quadrilateral formed by the points( 1, 2), (2, - 3), (-2, 4) and (0,5)​

= $\dfrac{1}{2} [1 (-3 -4)+2 (4-5)-2(5-2)+0(2+3)]$ square units

= $\dfrac{1}{2} [1 (-7)+2 (-1)-2(3)+0(5)]$ square units

= $\dfrac{1}{2} [-7-2-6]$ square units

= $\dfrac{1}{2} (-15)$ square units

= 7.5 square units

∴ The area of the quadrilateral formed by the points( 1, 2), (2, - 3), (-2, 4) and (0,5)​ = 7.5 square units