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प्रश्न
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
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उत्तर
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.
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संबंधित प्रश्न
Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0)
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)
Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by y-axis. Also, find the coordinates of the point of division in each case.
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.
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.
Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5, 6), B(1, –2) and C(3, –2).
If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
Find the area of triangle with vertices ( a, b+c) , (b, c+a) and (c, a+b).
The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are
If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =
What is the form of co-ordinates of a point on the X-axis?
Write the equations of the x-axis and y-axis.
Point (–3, 5) lies in the ______.
If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has ______.
If the points P(1, 2), Q(0, 0) and R(x, y) are collinear, then find the relation between x and y.
Given points are P(1, 2), Q(0, 0) and R(x, y).
The given points are collinear, so the area of the triangle formed by them is `square`.
∴ `1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = square`
`1/2 |1(square) + 0(square) + x(square)| = square`
`square + square + square` = 0
`square + square` = 0
`square = square`
Hence, the relation between x and y is `square`.
In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?
Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate of a point on y-axis is zero.
