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
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 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.
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
The line joining the points (2, 1) and (5, -8) is trisected at the points P and Q. If point P lies on the line 2x - y + k = 0. Find the value of k.
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
Find the coordinates of the midpoints of the line segment joining
P(-11,-8) and Q(8,-2)
Find the ratio in which the point (-1, y) lying on the line segment joining points A(-3, 10) and (6, -8) divides it. Also, find the value of y.
ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of one its diagonal.
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
The abscissa and ordinate of the origin are
The perpendicular distance of the P (4,3) from y-axis is
Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by the x-axis. Also, find the coordinates of the point of division.
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
what is the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\] .
If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is
If point P is midpoint of segment joining point A(– 4, 2) and point B(6, 2), then the coordinates of P are ______
Abscissa of all the points on the x-axis is ______.
The point at which the two coordinate axes meet is called the ______.
If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is ______.
