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Question
Find the co-ordinates of points of trisection of the line segment joining the point (6, –9) and the origin.
Solution
Let P and Q be the points of trisection of the line segment joining A(6, –9) and B(0, 0).
P divides AB in the ratio 1 : 2.
Therefore, the co-ordinates of point P are
`((1 xx 0 + 2 xx 6)/(1 + 2),(1 xx 0 + 2 xx (-9))/(2 + 1))`
=`(12/3, (-18)/3)`
= (4, −6)
Q divides AB in the ratio 2 : 1.
Therefore, the co-ordinates of point Q are
`((2 xx 0 + 1 xx 6)/(2 + 1),(2 xx 0 + 1 xx (-9))/(2 + 1))`
= `(6/3, (-9)/3)`
= (2, –3)
Thus, the required points are (4, −6) and (2, −3).
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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 -
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