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 follo
Answers
Given : Hockey field is rectangular in shape - 100 yards by 60 yards.
To Find : The coordinates of the centroid of ΔEHJ
If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by
The point on x axis equidistant from I and E is
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 point on y axis equidistant from B and C
Solution:
Centroid of ΔEHJ
E(2,1), H(-2,4) & J(-2,-2)
= (2 - 2 - 2)/3 , (1 + 4 - 2)/3
= -2/3 , 1
The coordinates of the centroid of ΔEHJ are (-2/3, 1)
A(3,6) and G(1,-3)
P will be mid point
Hence P ( 3 + 1)/2 , (6 - 3)/2
P ( 2 , 3/2)
position of P will be given by (2, 3/2)
The point on x axis equidistant from I and E be (x , 0)
I(-1,1) and E(2,1)
=> (x + 1)² + (0 - 1)² = (x - 2)² + (0 - 1)²
=> (x + 1)² = (x - 2)²
=> x² + 2x + 1 = x² - 4x + 4
=> 6x = 3
=> x = 1/2
(1/2 , 0)
The point on x axis equidistant from I and E is (1/2, 0)
distance from K(-4,1) is twice his distance from E(2,1)
KQ : QE = 2 : 1
Q = ( 2 * 2 + 1 *(-4))/(2 + 1) , ( 2 * 1 + 1 * 1)/(2 + 1)
=> Q = ( 0 , 1)
coordinates of the position of a player Q (0,1)
point on y axis (0, y) equidistant from B(4,3) and C(4,-1)
=>( 0 - 4)² + (y - 3)² = (0 - 4)² + ( y + 1)²
=> y² -6y + 9 = y² + 2y + 1
=> 8y = 9
=> y = 1
Hence The point on y axis equidistant from B and C is (0 , 1)
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