Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
The co-ordinates of the midpoint `(x_m, y_m)` between two points `(x_1, y_1)` and `(x_2, y_2)` is given by,
`(x_m,y_m) = (((x_1 + y_1)/2)"," ((y_1 + y_2)/2))`
In a parallelogram the diagonals bisect each other. That is the point of intersection of the diagonals is the midpoint of either of the diagonals.
Here, it is given that the vertices of a parallelogram are A(−2,−1), B(1,0) and C(4,3) and D(1,2).
We see that ‘AC’ and ‘BD’ are the diagonals of the parallelogram.
The midpoint of either one of these diagonals will give us the point of intersection of the diagonals.
Let this point be M(x, y).
Let us find the midpoint of the diagonal ‘AC’.
`(x_m, y_m) = (((-2 + 4)/2)","((-1+3)/2))`
`(x_m, y_m) = (((-2+4)/2)","((-1+3)/2))`
`(x_m, y_m) = (1,1)`
Hence the co-ordinates of the point of intersection of the diagonals of the given parallelogram are (1, 1).
APPEARS IN
संबंधित प्रश्न
The line segment joining the points P(3, 3) and Q(6, -6) is trisected at the points A and B such that Ais nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).
Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).
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.
Find the area of quadrilateral ABCD whose vertices are A(-5, 7), B(-4, -5) C(-1,-6) and D(4,5)
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
ABCD is a parallelogram with vertices \[A ( x_1 , y_1 ), B \left( x_2 , y_2 \right), C ( x_3 , y_3 )\] . Find the coordinates of the fourth vertex D in terms of \[x_1 , x_2 , x_3 , y_1 , y_2 \text{ and } y_3\]
If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c.
Write the condition of collinearity of points (x1, y1), (x2, y2) and (x3, y3).
The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =
If the points(x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =
If the centroid of the triangle formed by the points (3, −5), (−7, 4), (10, −k) is at the point (k −1), then k =
The ratio in which the line segment joining P (x1, y1) and Q (x2, y2) is divided by x-axis is
Find the point on the y-axis which is equidistant from the points (S, - 2) and (- 3, 2).
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`
What are the coordinates of origin?
The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are ______.
Which of the points P(0, 3), Q(1, 0), R(0, –1), S(–5, 0), T(1, 2) do not lie on the x-axis?
The coordinates of the point where the line 2y = 4x + 5 crosses x-axis is ______.
