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प्रश्न
Find the midpoint of the line segment joining the following pair of point :
(4,7) and (10,15)
उत्तर
Coordinates of P are
P (x , y) = P `((4 + 10)/2 , (7 + 15)/2)`
= P (7 , 11)
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संबंधित प्रश्न
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.
Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).
A(6, -2), B(3, -2) and C(S, 6) are the three vertices of a parallelogram ABCD. Find the coordinates of the fourth vertex c.
Point M is the mid-point of segment AB. If AB = 8.6 cm, then find AM.
The points A(−5, 4), B(−1, −2) and C(5, 2) are the vertices of an isosceles right-angled triangle where the right angle is at B. Find the coordinates of D so that ABCD is a square
The mid-point of the line joining (−a, 2b) and (−3a, −4b) is
In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally
Find coordinates of the midpoint of a segment joining point A(–1, 1) and point B(5, –7)
Solution: Suppose A(x1, y1) and B(x2, y2)
x1 = –1, y1 = 1 and x2 = 5, y2 = –7
Using midpoint formula,
∴ Coordinates of midpoint of segment AB
= `((x_1 + x_2)/2, (y_1+ y_2)/2)`
= `(square/2, square/2)`
∴ Coordinates of the midpoint = `(4/2, square/2)`
∴ Coordinates of the midpoint = `(2, square)`
If A(5, 4), B(–3, –2) and C(1, –8) are the vertices of a ∆ABC. Segment AD is median. Find the length of seg AD:
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).
