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प्रश्न
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.
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उत्तर
Distance between points (0,0) and (36,15)
= `sqrt((36-0)^2+(15-0)^2)`
= `sqrt(36^2+15^2)`
= `sqrt(1296+225)`
= `sqrt(1521)`
= `sqrt(39^2)`
= 39
Yes, we can find the distance between the given towns A and B.
Assume town A at origin point (0, 0).
Therefore, town B will be at point (36, 15) with respect to town A.
And hence, as calculated above, the distance between town A and B will be
39 km.
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संबंधित प्रश्न
If the point P(2, 2) is equidistant from the points A(−2, k) and B(−2k, −3), find k. Also find the length of AP.
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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 points
P(a sin ∝,a cos ∝ )and Q( acos ∝ ,- asin ∝)
Determine whether the points are collinear.
A(1, −3), B(2, −5), C(−4, 7)
If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance
2AB is equal to
Find the distance between the following pairs of point in the coordinate plane :
(7 , -7) and (2 , 5)
Find the distance of the following point from the origin :
(6 , 8)
Find the distance of the following point from the origin :
(0 , 11)
Find the distance between the following point :
(sin θ , cos θ) and (cos θ , - sin θ)
Prove that the following set of point is collinear :
(5 , 5),(3 , 4),(-7 , -1)
Find the distance between the points (a, b) and (−a, −b).
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.
Find distance between point A(– 3, 4) and origin O
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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:
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 (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).
Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.
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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.
