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प्रश्न
A( 4, 2), B(-2, -6) and C(l, 1) are the vertices of triangle ABC. Find its centroid and the length of the median through C.
उत्तर
Let G (a,b) be at centroid of Δ ABC ,
Coordinates of G are ,
G (a , b) = G = `((4 - 2 +1)/3 , (2 - 6 + 1)/3)` = G (1 , -1)
Let CE be the median through C
∴ AE : EB = 1 : 1
Coordinates of E are
E (x , y) = E `((4 - 2)/2 , (2 - 6)/2)` = E (1 , -2)
Length of median CE = `sqrt ((1 - 1)^2 + (2 - 1)^2)`
`= sqrt 9`
= 3 units
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Find the coordinates of point P if P divides the line segment joining the points A(–1, 7) and B(4, –3) in the ratio 2 : 3.
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Find the midpoint of the line segment joining the following pair of point :
( -3, 5) and (9, -9)
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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`
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⇒ x = – 6
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⇒ `square` + y = 0
⇒ y = 3
Hence coordinates of B is (– 6, 3).
