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प्रश्न
Two vertices of a triangle are ( -1, 4) and (5, 2). If the centroid is (0, 3), find the third vertex.
उत्तर
Let G be the centroid of Δ ABC whose coordinaes are (0 , -3) and let C (x , y) be the coordinates of thgird vertex
coordinates of G are ,
G (0 , -3) = G `((- 1 + 5 + "x")/3 , (4 + 2 + "y")/3)`
O = `(4 + "x")/3 , -3 = (6 + 4)/3`
x = -4 , y = - 15
Coordinates of third vertex are (-4 , - 15)
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संबंधित प्रश्न
Points A and B have co-ordinates (3, 5) and (x, y) respectively. The mid-point of AB is (2, 3). Find the values of x and y.
Points P(a, −4), Q(−2, b) and R(0, 2) are collinear. If Q lies between P and R, such that PR = 2QR, calculate the values of a and b.
Point P is the midpoint of seg AB. If co-ordinates of A and B are (-4, 2) and (6, 2) respectively then find the co-ordinates of point P.
(A) (-1,2) (B) (1,2) (C) (1,-2) (D) (-1,-2)
Find the midpoint of the line segment joining the following pair of point :
(4,7) and (10,15)
The midpoints of three sides of a triangle are (1, 2), (2, -3) and (3, 4). Find the centroid of the triangle.
The mid point of the line segment joining the points (p, 2) and (3, 6) is (2, q). Find the numerical values of a and b.
Find the mid-point of the line segment joining the points
(−2, 3) and (−6, −5)
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.
The ratio in which the x-axis divides the line segment joining the points A (a1, b1) and B (a2, b2) is
Find the coordinates of point P where P is the midpoint of a line segment AB with A(–4, 2) and B(6, 2).
Solution :
Suppose, (–4, 2) = (x1, y1) and (6, 2) = (x2, y2) and co-ordinates of P are (x, y).
∴ According to the midpoint theorem,
x = `(x_1 + x_2)/2 = (square + 6)/2 = square/2 = square`
y = `(y_1 + y_2)/2 = (2 + square)/2 = 4/2 = square`
∴ Co-ordinates of midpoint P are `square`.
