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प्रश्न
Three consecutive vertices of a parallelogram ABCD are A(S, 5), B(-7, -5) and C(-5, 5). Find the coordinates of the fourth vertex D.
उत्तर
we know that in a parallelogram diagonals bisect each other
∴ midpoint of AC = midpoint of BD
`"O" ((8 - 5)/2 , (5 + 5)/2) = "O"(("x" - 7)/2 , ("y" - 5)/2)`
`(8 - 5)/2 = ("x" - 7)/2 , (5 + 5)/2 = ("y" - 5)/2`
`3/2 = ("x" - 7)/2 , 10 = "y" - 5`
x = 10 , y = 15
Coordinates of fourth vertex D are (10 , 15)
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संबंधित प्रश्न
Find the mid-point of the line segment joining the points:
(5, –3) and (–1, 7)
A(5, 3), B(–1, 1) and C(7, –3) are the vertices of triangle ABC. If L is the mid-point of AB and M is the mid-point of AC, show that : `LM = 1/2 BC`.
One end of the diameter of a circle is (–2, 5). Find the co-ordinates of the other end of it, if the centre of the circle is (2, –1).
Find the midpoint of the line segment joining the following pair of point :
( a+3, 5b), (3a-1, 3b +4).
If (-3, 2), (1, -2) and (5, 6) are the midpoints of the sides of a triangle, find the coordinates of the vertices of the triangle.
The midpoint of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a+1). Find the value of a and b.
show that the points A(- 1, 2), B(2, 5) and C(- 5, – 2) are collinear.
Find the mid-point of the line segment joining the points
(a, b) and (a + 2b, 2a – b)
If the mid-point (x, y) of the line joining (3, 4) and (p, 7) lies on 2x + 2y + 1 = 0, then what will be the value of p?
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
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`
