Advertisements
Advertisements
प्रश्न
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
Advertisements
उत्तर
By joining P and R, we get two triangles PQR and PRS.
`"let" P (x_1, y_1) = P (-5,-3) , Q(x_2,y_2) = Q(-4,-6), R (x_3,y_3) = R(2,-3) and . Then S(x_4,y_4) = S(1,2)`
`"Area of " ΔPQR = 1/2 [ x_1 (y_2-y_3) +x_2(y_3-y_1)+x_3 (y_1-y_2)]`
`=1/2 [-5(-6+3)-4(-3+3)+2(-3+6)}`
`=1/2 [15-0+6]=21/2 sq. units`
`"Area of "Δ PRS = 1/2 [ x_1(y_3-y_4) +x_3 (y_4-y_1)+x_4(y_1-y_3)]`
`=1/2[-5(-3-2)+2(2+3)+1(-3+3)]`
`=1/2[25+10+0]=35/2 sq. units`
So, the area of the quadrilateral PQRS is `21/2+35/2=28 ` sq. units
APPEARS IN
संबंधित प्रश्न
How will you describe the position of a table lamp on your study table to another person?
If G be the centroid of a triangle ABC, prove that:
AB2 + BC2 + CA2 = 3 (GA2 + GB2 + GC2)
A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.
The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.
Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by x-axis Also, find the coordinates of the point of division in each case.
In what ratio does the point P(2,5) divide the join of A (8,2) and B(-6, 9)?
In what ratio is the line segment joining A(2, -3) and B(5, 6) divide by the x-axis? Also, find the coordinates of the pint of division.
A point whose abscissa and ordinate are 2 and −5 respectively, lies in
what is the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\] .
If P (2, 6) is the mid-point of the line segment joining A(6, 5) and B(4, y), find y.
If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
If (−1, 2), (2, −1) and (3, 1) are any three vertices of a parallelogram, then
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
The distance of the point (4, 7) from the y-axis is
The line segment joining the points A(2, 1) and B (5, - 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x - y + k= 0 find the value of k.
The points (–5, 2) and (2, –5) lie in the ______.
Seg AB is parallel to X-axis and coordinates of the point A are (1, 3), then the coordinates of the point B can be ______.
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
The distance of the point (3, 5) from x-axis (in units) is ______.
