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प्रश्न
Find the distance between the points
A(1,-3) and B(4,-6)
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उत्तर
A(1,-3) and B(4,-6)
The given points are A(1,-3) and B(4,-6 )
`Then (x_1 =1,y_1=-3) and (x_2 = 4, y_2=-6)`
`AB = sqrt((x_2-x_1)^2 +(y_2-y_1)^2)`
`=sqrt((4-1)^2+{-6-(-3)}^2)`
`=sqrt((4-1)^2 + (-6+3)^2)`
`= sqrt((3)^2 +(-3)^2`
`= sqrt(9+9)`
`=sqrt(18)`
`=sqrt(9xx2)`
`=3 sqrt(2) ` units
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संबंधित प्रश्न
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
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If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Prove that the points A(1, 7), B (4, 2), C(−1, −1) D (−4, 4) are the vertices of a square.
Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.
Find the distance of the following points from the origin:
(iii) C (-4,-6)
Find all possible values of y for which distance between the points is 10 units.
Find the distance between the following pair of points.
L(5, –8), M(–7, –3)
AB and AC are the two chords of a circle whose radius is r. If p and q are
the distance of chord AB and CD, from the centre respectively and if
AB = 2AC then proove that 4q2 = p2 + 3r2.
Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.
Prove that the points (5 , 3) , (1 , 2), (2 , -2) and (6 ,-1) are the vertices of a square.
Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.
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The length of line PQ is 10 units and the co-ordinates of P are (2, -3); calculate the co-ordinates of point Q, if its abscissa is 10.
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
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 x axis equidistant from I and E is ______.
The distance of the point (5, 0) from the origin is ______.
