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प्रश्न
The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is ______.
पर्याय
(0, 0)
(0, 2)
(2, 0)
(–2, 0)
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उत्तर
The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is (0, 0).
Explanation:
We know that, the perpendicular bisector of the any line segment divides the segment into two equal parts i.e., the perpendicular bisector of the line segment always passes through the mid-point of the line segment.
Mid-point of the line segment joining the points A(–2, –5) and B(2, 5)
= `((-2 + 2)/2, (-5 + 5)/2)` ...`["Since, mid-point of any line segment which passes through the points" (x_1, y_1) "and" (x_2, y_2) = ((x_1 + x_2)/2, (y_1 + y_2)/2)]`
= (0, 0)
Hence, (0, 0) is the required point lies on the perpendicular bisector of the lines segment.
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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:
The coordinates of the centroid of ΔEHJ are ______.
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:
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