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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 the point P(2, 2) is equidistant from the points A(−2, k) and B(−2k, −3), find k. Also find the length of AP.
If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
If a≠b≠0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.
Given a line segment AB joining the points A(–4, 6) and B(8, –3). Find
1) The ratio in which AB is divided by y-axis.
2) Find the coordinates of the point of intersection.
3) The length of AB.
Using the distance formula, show that the given points are collinear:
(-2, 5), (0,1) and (2, -3)
Determine whether the points are collinear.
L(–2, 3), M(1, –3), N(5, 4)
Find the distance between the following pairs of point in the coordinate plane :
(7 , -7) and (2 , 5)
Find the distance between the following point :
(sin θ , cos θ) and (cos θ , - sin θ)
Find the distance of a point (13 , -9) from another point on the line y = 0 whose abscissa is 1.
Prove that the points (1 ,1),(-4 , 4) and (4 , 6) are the certices of an isosceles triangle.
A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Given A = (3, 1) and B = (0, y - 1). Find y if AB = 5.
Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.
Find distance of point A(6, 8) from origin
Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?
The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
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:
The point on x axis equidistant from I and E is ______.
