Advertisements
Advertisements
Question
Prove that the diagonals of a rectangle ABCD with vertices A(2,-1), B(5,-1) C(5,6) and D(2,6) are equal and bisect each other
Advertisements
Solution
The vertices of the rectangle ABCD are A(2, -1), B(5, -1), C(5, 6) and D(2, 6) Now,
`"Coordinates of midpoint of" AC = ((2+5)/2 , (-1+6)/2) = (7/5 ,5/2)`
`"Coordinates of midpoint of " BD = ((5+2)/2 , (-1+6)/2)= (7/2,5/2)`
Since, the midpoints of AC and BD coincide, therefore the diagonals of rectangle ABCD bisect each other.
RELATED QUESTIONS
On which axis do the following points lie?
P(5, 0)
Find the centre of the circle passing through (5, -8), (2, -9) and (2, 1).
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
Find the points on the y-axis which is equidistant form the points A(6,5) and B(- 4,3)
If (2, p) is the midpoint of the line segment joining the points A(6, -5) and B(-2,11) find the value of p.
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
The abscissa of any point on y-axis is
If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.
If (x, y) be on the line joining the two points (1, −3) and (−4, 2) , prove that x + y + 2= 0.
Find the value of k, if the points A(7, −2), B (5, 1) and C (3, 2k) are collinear.
If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a), then prove that x + y = a + b.
Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
what is the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\] .
If (−1, 2), (2, −1) and (3, 1) are any three vertices of a parallelogram, then
If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =
If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is
What is the form of co-ordinates of a point on the X-axis?
(–1, 7) is a point in the II quadrant.
Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
