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प्रश्न
Two vertices of a triangle are (1, 4) and (3, 1). If the centroid of the triangle is the origin, find the third vertex.
उत्तर
Given the centroid of Δ ABC is at origin , i.e. G (0 , 0).
Let the coordinates of third vertex be (x , y).
Coordinates of G are ,
G (0 , 0) = G `((1 + 3 + "x")/3 , (4 + 1 + "y")/3)`
O = `(4 + "x")/2` , O = `(5 + "y")/2`
x = - 4 , y = -5
Coordinates of third vertex are (-4 , -5)
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संबंधित प्रश्न
Given M is the mid-point of AB, find the co-ordinates of A; if M = (1, 7) and B = (–5, 10).
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.
Find the midpoint of the line segment joining the following pair of point :
(a+b, b-a) and (a-b, a+b)
Find the length of the median through the vertex A of triangle ABC whose vertices are A (7, -3), B(S, 3) and C(3, -1).
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.
In what ratio does the point Q(1, 6) divide the line segment joining the points P(2, 7) and R(−2, 3)
Find the coordinates of midpoint of segment joining (22, 20) and (0, 16)
If A(5, 4), B(–3, –2) and C(1, –8) are the vertices of a ∆ABC. Segment AD is median. Find the length of seg AD:
Point M (2, b) is the mid-point of the line segment joining points P (a, 7) and Q (6, 5). Find the values of ‘a’ and ‘b’.
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).
