Advertisements
Advertisements
प्रश्न
Find the area of a quadrilateral ABCD whose vertices area A(3, -1), B(9, -5) C(14, 0) and D(9, 19).
Advertisements
उत्तर
By joining A and C, we get two triangles ABC and ACD. Let
`A(x_1,y_1)=A(3,-1),B(x_2,y_2)=B(9,-5),C(x_3,y_3)=C(14,0) and D(x_4 , y_4 ) = D(9,19)`
Then,
`"Area of" ΔABC = 1/2 [ x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1 - y_2)]`
`=1/2 [ 3(-5-0) +9(0+1)+14(-1+5)]`
`=1/2 [-15+9+56] = 25` sq.units
`Area of ΔACD = 1/2 [ x_1 (y_3-y_4)+x_3(y_4-y_1)+x_4(y_1-y_3)]`
`=1/2 [ 3(0-19)+14(19+1)+9(-1-0)]`
`=1/2 [ -57 +280-9] = 107 sq. units`
So, the area of the quadrilateral is 25 +107 =132 sq . units.
APPEARS IN
संबंधित प्रश्न
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.
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.
Find the coordinates of the point which divides the line segment joining (−1,3) and (4, −7) internally in the ratio 3 : 4
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
Find the value of a, so that the point ( 3,a ) lies on the line represented by 2x - 3y =5 .
Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.
Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
If (x , 2), (−3, −4) and (7, −5) are collinear, then x =
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
If (−2, 1) is the centroid of the triangle having its vertices at (x , 0) (5, −2), (−8, y), then x, y satisfy the relation
The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be
The coordinates of the point P dividing the line segment joining the points A (1, 3) and B(4, 6) in the ratio 2 : 1 are
Find the coordinates of the point of intersection of the graph of the equation x = 2 and y = –3.
Signs of the abscissa and ordinate of a point in the second quadrant are respectively.
If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has ______.
Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.
Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
