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प्रश्न
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
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उत्तर
Distance between two points (x1, y1) ( x2, y2) is:
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
Distance between A(–3, –14) and B(a, –5) is:
d = `sqrt([(a + 3)^2 + (-5 + 14)^2])` = 9
Squaring on L.H.S and R.H.S.
(a + 3)2 + 81 = 81
(a + 3)2 = 0
(a + 3)(a + 3) = 0
a + 3 = 0
a = –3
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संबंधित प्रश्न
If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Find the distance between the points
A(1,-3) and B(4,-6)
Find the distance of the following points from the origin:
(ii) B(-5,5)
Find the distance between the following pair of point.
T(–3, 6), R(9, –10)
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.
Find the distance of a point (7 , 5) from another point on the x - axis whose abscissa is -5.
Find the distance between the origin and the point:
(-8, 6)
Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.
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.
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
Find the point on y-axis whose distances from the points A (6, 7) and B (4, -3) are in the ratio 1: 2.
Calculate the distance between A (7, 3) and B on the x-axis, whose abscissa is 11.
By using the distance formula prove that each of the following sets of points are the vertices of a right angled triangle.
(i) (6, 2), (3, -1) and (- 2, 4)
(ii) (-2, 2), (8, -2) and (-4, -3).
Find distance CD where C(– 3a, a), D(a, – 2a)
Using distance formula decide whether the points (4, 3), (5, 1), and (1, 9) are collinear or not.
The distance of the point (α, β) from the origin 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:
The point on x axis equidistant from I and E is ______.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
