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प्रश्न
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
विकल्प
right triangle
isosceles triangle
equilateral triangle
scalene triangle
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उत्तर
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a isosceles triangle.
Explanation:
Let A(– 4, 0), B(4, 0), C(0, 3) are the given vertices.
Now, distance between A(– 4, 0) and B(4, 0),
AB = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt([4 - (-4)]^2 + (0 - 0)^2`
= `sqrt((4 + 4)^2`
= `sqrt(8^2)`
= 8
Distance between B(4, 0) and C(0, 3),
BC = `sqrt((0 - 4)^2 + (3 - 0)^2`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5
Distance between A(– 4, 0) and C(0, 3),
AC = `sqrt([0 - (-4)]^2 + (3 - 0)^2`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5
∵ BC = AC
Hence, ΔABC is an isosceles triangle because an isosceles triangle has two sides equal.
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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:
If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.
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?
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 point on y axis equidistant from B and C is ______.
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Find distance between points P(– 5, – 7) and Q(0, 3).
By distance formula,
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= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
