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प्रश्न
Find the midpoint of the line segment joining the following pair of point :
(3a-2b, Sa+7b) and (a+4b, a-3b)
उत्तर
Coordinates of C are ,
C (x , y) = C `(("a + 4b + 3a - 2b")/2 , ("a - 3b + 5a + 7b")/2)`
= C (2a + b , 3a + 2b)
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संबंधित प्रश्न
M is the mid-point of the line segment joining the points A(–3, 7) and B(9, –1). Find the coordinates of point M. Further, if R(2, 2) divides the line segment joining M and the origin in the ratio p : q, find the ratio p : q.
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The points A(−3, 6), B(0, 7) and C(1, 9) are the mid-points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallelogram.
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Find coordinates of midpoint of segment joining (– 2, 6) and (8, 2)
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`
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