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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
Find the distance between the following pairs of points:
(2, 3), (4, 1)
If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
Find the distance of the following points from the origin:
(iii) C (-4,-6)
Using the distance formula, show that the given points are collinear:
(-1, -1), (2, 3) and (8, 11)
Find the distances between the following point.
P(–6, –3), Q(–1, 9)
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Find the distance of the following point from the origin :
(8 , 15)
Find the distance of a point (13 , -9) from another point on the line y = 0 whose abscissa is 1.
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
Find the distance between the points (a, b) and (−a, −b).
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
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.
Find the distance of the following points from origin.
(a cos θ, a sin θ).
Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.
The distance between the points A(0, 6) and B(0, -2) 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 ______.
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
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.
Find distance between points P(– 5, – 7) and Q(0, 3).
By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
