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प्रश्न
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
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उत्तर
We know that any point on x-axis has coordinates of the form (x, 0).
Abscissa of point B = 11
Since, B lies of x-axis, so its co-ordinates are (11, 0).
AB = `sqrt((11 -7)^2 + (0 -3)^2)`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5 units
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संबंधित प्रश्न
Find the distance between the following pairs of points:
(−5, 7), (−1, 3)
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The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.
Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.
A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.
The length of line PQ is 10 units and the co-ordinates of P are (2, -3); calculate the co-ordinates of point Q, if its abscissa is 10.
Use distance formula to show that the points A(-1, 2), B(2, 5) and C(-5, -2) are collinear.
If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.
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:
What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear?
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
