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प्रश्न
Points A(–5, x), B(y, 7) and C(1, –3) are collinear (i.e. lie on the same straight line) such that AB = BC. Calculate the values of x and y.
उत्तर
Given, AB = BC, i.e., B is the mid-point of AC.
∴ `(y, 7) = ((-5 + 1)/2, (x - 3)/2)`
`(y, 7) = (-2, (x - 3)/2)`
`=> y = -2` and `7 = (x - 3)/2`
`=>` y = –2 and x = 17
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संबंधित प्रश्न
Find the mid-point of the line segment joining the points:
(–6, 7) and (3, 5)
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Calculate the co-ordinates of the centroid of the triangle ABC, if A = (7, –2), B = (0, 1) and C =(–1, 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.
Find the mid-point of the line segment joining the points
(−2, 3) and (−6, −5)
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?
O(0, 0) is the centre of a circle whose one chord is AB, where the points A and B are (8, 6) and (10, 0) respectively. OD is the perpendicular from the centre to the chord AB. Find the coordinates of the mid-point of OD.
A(−3, 2), B(3, 2) and C(−3, −2) are the vertices of the right triangle, right angled at A. Show that the mid-point of the hypotenuse is equidistant from the vertices
Find the co-ordinates of centroid of a triangle if points D(–7, 6), E(8, 5) and F(2, –2) are the mid-points of the sides of that triangle.
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`
⇒ `square = square` + x
⇒ x = `square - square`
⇒ x = – 6
and `square = (square + y)/2`
⇒ `square` + y = 0
⇒ y = 3
Hence coordinates of B is (– 6, 3).
