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प्रश्न
Read the following passage:
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Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.
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Based on the above information, answer the following questions:
- Find the coordinates of the point of intersection of diagonals AC and BD.
- Find the length of the diagonal AC.
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- Find the area of the campaign Board ABCD.
OR - Find the ratio of the length of side AB to the length of the diagonal AC.
- Find the area of the campaign Board ABCD.
उत्तर
We have, A(1, 1), B(7, 1), (7, 5), D(1, 5)
From these coordinates it is clear that the board is in the shape of rectangle
- Point of intersection of diagonals is their midpoint
So, `[((1 + 7))/2, ((1 + 5))/2]` = (4, 3) - Length of diagonal AC
AC = `sqrt((7 - 1)(7 - 1) + (5 - 1)(5 - 1))= sqrt(52)` units -
- Area of campaign board
= 6 × 4
= 24 units square
OR - Ratio of lengths = `("AB")/("AC")`
= `6/sqrt(52)`
= `6 : sqrt(52)`
- Area of campaign board
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संबंधित प्रश्न
Find the distance between the following pairs of points:
(−5, 7), (−1, 3)
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.
ABC is a triangle and G(4, 3) is the centroid of the triangle. If A = (1, 3), B = (4, b) and C = (a, 1), find ‘a’ and ‘b’. Find the length of side BC.
Prove that the points A(1, 7), B (4, 2), C(−1, −1) D (−4, 4) are the vertices of a square.
Find the distances between the following point.
A(a, 0), B(0, a)
Find the distances between the following point.
R(–3a, a), S(a, –2a)
A line segment of length 10 units has one end at A (-4 , 3). If the ordinate of te othyer end B is 9 , find the abscissa of this end.
Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.
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:
What are the 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?
If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.
