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प्रश्न
Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).
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उत्तर
Let the coordinates of the point on x-axis be (x, 0).
From the given information, we have:
`sqrt((x -11)^2 + (0 + 8)^2)` = 17
(x - 11)2 + (0 + 8)2 = 289
x2 + 121 - 22x + 64 = 289
x2 - 22x - 104 = 0
x2 - 26x + 4x - 104 = 0
x(x - 26) + 4(x - 26) = 0
(x - 26)(x + 4) = 0
x = 26, -4
Thus, the required co-ordinates of the points on x-axis are (26, 0) and (-4, 0).
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संबंधित प्रश्न
Find the distance between the following pairs of points:
(a, b), (−a, −b)
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Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.
x (1,2),Y (3, -4) and z (5,-6) are the vertices of a triangle . Find the circumcentre and the circumradius of the triangle.
ABCD is a square . If the coordinates of A and C are (5 , 4) and (-1 , 6) ; find the coordinates of B and D.
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______
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Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.
The distance of the point P(–6, 8) from the origin is ______.
What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?
