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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
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.
Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.
Find the distance between the points
(ii) A(7,-4)and B(-5,1)
Find the distance between the points
A(-6,-4) and B(9,-12)
Using the distance formula, show that the given points are collinear:
(1, -1), (5, 2) and (9, 5)
Determine whether the points are collinear.
A(1, −3), B(2, −5), C(−4, 7)
Find the distances between the following point.
R(–3a, a), S(a, –2a)
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
Find the distance of the following point from the origin :
(0 , 11)
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.
Find the distance between the following pair of points:
`(sqrt(3)+1,1)` and `(0, sqrt(3))`
The distance between the points (3, 1) and (0, x) is 5. Find x.
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
Show that each of the triangles whose vertices are given below are isosceles :
(i) (8, 2), (5,-3) and (0,0)
(ii) (0,6), (-5, 3) and (3,1).
The distance between points P(–1, 1) and Q(5, –7) is ______.
The distance of the point (α, β) from the origin 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:
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?
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
