Find the area of the quadrilateral formed by the points (1, 2), (2,-3), (-2, 4), (0, 5) taken in order.
Answers
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})]21[x1(y2−y3)+x2(y3−y4)+x3(y4−y1)+x4(y1−y2)]
∴ 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)]21[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)]21[1(−7)+2(−1)−2(3)+0(5)] square units
= \dfrac{1}{2} [-7-2-6]21[−7−2−6] square units
= \dfrac{1}{2} (-15)21(−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