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प्रश्न
The centre ‘O’ of a circle has the coordinates (4, 5) and one point on the circumference is (8, 10). Find the coordinates of the other end of the diameter of the circle through this point.
उत्तर
Let (x, y) be the coordinates of the other end of the diameter of the circle.
Since, centre is the midpoint of the diameter of the circle.
So coordinates of midpoint of diameter
AB = `((8 + x)/2 , (10 + y)/2)`
But O(4, 5) is the centre hence
`(8 + x)/2` = 4
⇒ x = 8 - 8 = 0.
Also `(10 + y)/2` = 5
⇒ y = 10 - 10 = 0.
Hence (0, 0) be the coordinates of the other end.
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संबंधित प्रश्न
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The coordinates of diameter AB of a circle are A(2, 7) and B(4, 5), then find the coordinates of the centre
From the figure given alongside, find the length of the median AD of triangle ABC. Complete the activity.
Solution:
Here A(–1, 1), B(5, – 3), C(3, 5) and suppose D(x, y) are coordinates of point D.
Using midpoint formula,
x = `(5 + 3)/2`
∴ x = `square`
y = `(-3 + 5)/2`
∴ y = `square`
Using distance formula,
∴ AD = `sqrt((4 - square)^2 + (1 - 1)^2`
∴ AD = `sqrt((square)^2 + (0)^2`
∴ AD = `sqrt(square)`
∴ The length of median AD = `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:
