Advertisements
Advertisements
प्रश्न
Find the area of quadrilateral ABCD whose vertices are A(-3, -1), B(-2,-4) C(4,-1) and D(3,4)
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(-2,-4) , C(x_3,y_3) = C(4,-1) and Then D (x_4,y_4)= D(3,4)`
`"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 [-3(-4+1)-2(-1+1)+4(-1+4)]`
`=1/2 [9-0+12]=21/2 ` 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(-1-4)+4(4+1)+3(-1+1)]`
`=1/2 [15+20+0]=35/2` sq. units
So, the area of the quadrilateral ABCD is `21/2+35/2=28 `.sq units sq units
APPEARS IN
संबंधित प्रश्न
The base PQ of two equilateral triangles PQR and PQR' with side 2a lies along y-axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R' of the triangles.
Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
Find the points of trisection of the line segment joining the points:
(2, -2) and (-7, 4).
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
Find the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8) Also, find the value of m.
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k.
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
Find the ratio in which the line segment joining the points A (3, 8) and B (–9, 3) is divided by the Y– axis.
Find the coordinates of the circumcentre of a triangle whose vertices are (–3, 1), (0, –2) and (1, 3).
ΔXYZ ∼ ΔPYR; In ΔXYZ, ∠Y = 60o, XY = 4.5 cm, YZ = 5.1 cm and XYPY =` 4/7` Construct ΔXYZ and ΔPYR.
Write the coordinates of a point on X-axis which is equidistant from the points (−3, 4) and (2, 5).
If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 + b3 + c3 =
If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =
If P is a point on x-axis such that its distance from the origin is 3 units, then the coordinates of a point Q on OY such that OP = OQ, are
In the above figure, seg PA, seg QB and RC are perpendicular to seg AC. From the information given in the figure, prove that: `1/x + 1/y = 1/z`
If y-coordinate of a point is zero, then this point always lies ______.
