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प्रश्न
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
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उत्तर
Let the co-ordinates of the required point on y-axis be P (0, y).
The given points are A (5, 2) and B (-4, 3).
Given, PA = PB
PA2 = PB2
(0 -5)2 + (y -2)2 = (0 + 4)2 + (y - 3)2
25 + y2 + 4 - 4y = 16 + y2 + 9 - 6y
2y = -4
y = -2
Thus, the required point is (0, -2).
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संबंधित प्रश्न
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.
Using the distance formula, show that the given points are collinear:
(1, –1), (5, 2) and (9, 5)
Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius.
Find the distance between the origin and the point:
(8, −15)
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.
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:
The point on y axis equidistant from B and C is ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
