Advertisements
Advertisements
Question
Find the area of quadrilateral ABCD whose vertices are A(-5, 7), B(-4, -5) C(-1,-6) and D(4,5)
Solution
By joining A and C, we get two triangles ABC and ACD .
`" let" A (x_1,y_1)=A(-5,7) , B(x_2,y_2) = B(-4,-5) , C (x_3,y_3) = c (-1,-6) and D(x_4,y_4) = D(4,5)`
Then
`"Area of" Δ ABC = 1/2 [ x_1 (y_2 -y_3) +x_2 (y_3-y_1) +x_3(y_1-y_2)]`
`=1/2[-5(-5+6)-4(-6-7)-1(7+5)]`
`=1/2[-5+52-12]=35/2` sq. units
`"Area of" Δ ACD = 1/2 [x_1(y_3-y_4)+x_3(y_4-y_1)+x_4(y_1-y_3)]`
`=1/2 [-5(-6-5)-1(5-7)+4(7+6)]`
`=1/2[55+2+52]=109/2 `sq. units
So, the area of the quadrilateral ABCD is `35/2+109/2=72 ` sq .units.
APPEARS IN
RELATED QUESTIONS
Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
If (−2, 3), (4, −3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.
Find the coordinates of the point which divides the line segment joining (−1,3) and (4, −7) internally in the ratio 3 : 4
Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and(1, 2) meet
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
If the poin A(0,2) is equidistant form the points B (3, p) and C (p ,5) find the value of p. Also, find the length of AB.
If the point A (4,3) and B ( x,5) lies on a circle with the centre o (2,3) . Find the value of x.
The line segment joining A( 2,9) and B(6,3) is a diameter of a circle with center C. Find the coordinates of C
If the points P (a,-11) , Q (5,b) ,R (2,15) and S (1,1). are the vertices of a parallelogram PQRS, find the values of a and b.
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, -3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.
Find the area of a quadrilateral ABCD whose vertices area A(3, -1), B(9, -5) C(14, 0) and D(9, 19).
If the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p.
If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p.
Find the value(s) of k for which the points (3k − 1, k − 2), (k, k − 7) and (k − 1, −k − 2) are collinear.
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =
If A (2, 2), B (−4, −4) and C (5, −8) are the vertices of a triangle, than the length of the median through vertex C is
The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are
(–1, 7) is a point in the II quadrant.
Co-ordinates of origin are ______.
