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प्रश्न
Find distance between points P(– 5, – 7) and Q(0, 3).
By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
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उत्तर
By distance formula,
PQ = `sqrt(bb((x^2 - x_1)^2) + (y_2 - y_1)^2`
= `sqrt(bb(0 - (-5)^2) + bb(3 - (-7)^2))`
= `sqrt(bb((5)^2) + bb((10)^2))`
= `sqrt(bb25 + bb100)`
= `sqrt(125)`
= `5sqrt(5)`
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संबंधित प्रश्न
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
If the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
If a≠b≠0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.
Find the distance between the following pair of points:
(-6, 7) and (-1, -5)
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 A(1, 7), B (4, 2), C(−1, −1) D (−4, 4) are the vertices of a square.
Find the distance between the following pair of point.
T(–3, 6), R(9, –10)
Prove that the points (6 , -1) , (5 , 8) and (1 , 3) are the vertices of an isosceles triangle.
Find the distance between the following pairs of points:
`(3/5,2) and (-(1)/(5),1(2)/(5))`
A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.
Given A = (x + 2, -2) and B (11, 6). Find x if AB = 17.
Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______
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:
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?
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
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Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane. |
- At an instance, the midfielders and forward formed a parallelogram. Find the position of the central midfielder (D) if the position of other players who formed the parallelogram are :- A(1, 2), B(4, 3) and C(6, 6)
- Check if the Goal keeper G(–3, 5), Sweeper H(3, 1) and Wing-back K(0, 3) fall on a same straight line.
[or]
Check if the Full-back J(5, –3) and centre-back I(–4, 6) are equidistant from forward C(0, 1) and if C is the mid-point of IJ. - If Defensive midfielder A(1, 4), Attacking midfielder B(2, –3) and Striker E(a, b) lie on the same straight line and B is equidistant from A and E, find the position of E.
