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प्रश्न
If the point A(x,2) is equidistant form the points B(8,-2) and C(2,-2) , find the value of x. Also, find the value of x . Also, find the length of AB.
उत्तर
As per the question
AB = AC
`⇒ sqrt((x-8)^2+(2+2)^2 ) = sqrt((x-2)^2 +(2+2)^2)`
Squaring both sides, we get
`(x-8)^2 +4^2 = (x - 2)^2 +4^2`
`⇒ x^2 -16x+64+16=x^2+4-4x+16`
`⇒ 16x-4x=64-4`
`⇒ x = 60/12=5`
Now,
`AB = sqrt((x-8)^2 +(2+2)^2)`
`= sqrt((5-8)^2 +(2+2)^2) (∵ x =2)`
`=sqrt((-3)^2 +(4)^2)`
`=sqrt(9+16) = sqrt(25)=5`
Hence, x = 5and AB = 5 units.
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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.
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- Fullbacks: As shown by players H, I and J.
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Using the picture of a hockey field below, answer the questions that follow:
The coordinates of the centroid of ΔEHJ are ______.
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