Question 46 (Case Based Question) - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

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-

The coordinates of the centroid of ΔEHJ are
(a) ((-2)/3,1) (b) (1, (-2)/3) (c) (2/3, 1) (d) (2/3, -1)

Transcript

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:
Marking coordinates of points
Question 46 The coordinates of the centroid of ΔEHJ are (a) ((−2)/3,1) (b) (1, (−2)/3) (c) (2/3, 1) (d) (2/3, −1)
Now,
Coordinates of centroid = ((𝑥_1 + 𝑥_2 + 𝑥_3)/3,(𝑦_1 + 𝑦_2+ 𝑦_3)/3)
= ((𝟐 + (−𝟐)+ (−𝟐))/𝟑,(𝟏 + 𝟒 + (−𝟐))/𝟑)
= ((−𝟐)/𝟑,𝟑/𝟑)
= ((−𝟐)/𝟑,𝟏)
So, the correct answer is (a)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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