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प्रश्न
A(–1, 0), B(1, 3) and D(3, 5) are the vertices of a parallelogram ABCD. Find the co-ordinates of vertex C.
उत्तर
Let the co-ordinates of vertex C be (x, y).
ABCD is a parallelogram.
∴ Mid-point of AC = Mid-point of BD
`((-1 + x)/2, (0 + y)/2) = ((1 + 3)/2, (3 + 5)/2)`
`((-1 + x)/2, y/2) = (2,4)`
`(-1 + x)/2 = 2 and y/2 = 4`
`x = 5` and `y/2 = 4`
x = 5 and y = 8
Thus, the co-ordinates of vertex C is (5, 8).
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संबंधित प्रश्न
ABCD is a parallelogram where A(x, y), B(5, 8), C(4, 7) and D(2, -4). Find
1) Coordinates of A
2) An equation of diagonal BD
Given M is the mid-point of AB, find the co-ordinates of B; if A = (3, –1) and M = (–1, 3).
P(4, 2) and Q(–1, 5) are the vertices of parallelogram PQRS and (–3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S.
The mid-point of the line segment joining (2a, 4) and (–2, 2b) is (1, 2a + 1). Find the values of a and b.
In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(–2, –5), Q(4, 3), a : b = 3 : 4
Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, –3) and (–2, 0) respectively.
Find the midpoint of the line segment joining the following pair of point :
( -3, 5) and (9, -9)
A lies on the x - axis amd B lies on the y -axis . The midpoint of the line segment AB is (4 , -3). Find the coordinates of A and B .
Find the coordinates of the mid-point of the line segment with points A(– 2, 4) and B(–6, –6) on both ends.
Point P is the centre of the circle and AB is a diameter. Find the coordinates of points B if coordinates of point A and P are (2, – 3) and (– 2, 0) respectively.
Given: A`square` and P`square`. Let B (x, y)
The centre of the circle is the midpoint of the diameter.
∴ Mid point formula,
`square = (square + x)/square`
⇒ `square = square` + x
⇒ x = `square - square`
⇒ x = – 6
and `square = (square + y)/2`
⇒ `square` + y = 0
⇒ y = 3
Hence coordinates of B is (– 6, 3).
