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प्रश्न
AB is a diameter of a circle with centre 0. If the ooordinates of A and 0 are ( 1, 4) and (3, 6 ). Find the ooordinates of B and the length of the diameter.
उत्तर
O is the centre of the circle with diameter AB .
∴ AO : OB = 1 : 1
Coordinnates of O are ,
O (3 , 6) = O `((1 + "x")/2 , (4 + "y")/2)`
`3 = (1 + "x")/2 , 6 = (4 + "y")/2`
6 = 1 + x , 12 = 4 + y
x = 5 , y = 8
Coordinates of B are (5 , 8)
Length of AB = `sqrt ((5 - 1)^2 + (8 - 4)^2)`
`= sqrt (16 + 16) = 4 sqrt 2` units
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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`
