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प्रश्न
What is the distance of the point (– 5, 4) from the origin?
विकल्प
3 units
`sqrt(14)` units
`sqrt(31)` units
`sqrt(41)` units
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उत्तर
`sqrt(41)` units
Explanation:
Given points are (– 5, 4) and (0, 0).
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
Here, x1 = – 5, y1 = 4, x2 = 0, y2 = 0
∴ Distance = `sqrt((0 - (- 5))^2 + (0 - 4)^2`
= `sqrt(5^2 + 4^2)`
= `sqrt(25 + 16)`
= `sqrt(41)`
Thus, the distance is `sqrt(41)` units.
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संबंधित प्रश्न
If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.
Given a triangle ABC in which A = (4, −4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2. Find the length of line segment AP.
Find value of x for which the distance between the points P(x,4) and Q(9,10) is 10 units.
Determine whether the points are collinear.
A(1, −3), B(2, −5), C(−4, 7)
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
A line segment of length 10 units has one end at A (-4 , 3). If the ordinate of te othyer end B is 9 , find the abscissa of this end.
Prove that the following set of point is collinear :
(5 , 5),(3 , 4),(-7 , -1)
ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.
Find the distance between the origin and the point:
(-8, 6)
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.
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.
Points A (-3, -2), B (-6, a), C (-3, -4) and D (0, -1) are the vertices of quadrilateral ABCD; find a if 'a' is negative and AB = CD.
Given A = (3, 1) and B = (0, y - 1). Find y if AB = 5.
Find the distance of the following points from origin.
(a cos θ, a sin θ).
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
Find distance between point A(–1, 1) and point B(5, –7):
Solution: Suppose A(x1, y1) and B(x2, y2)
x1 = –1, y1 = 1 and x2 = 5, y2 = –7
Using distance formula,
d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
∴ d(A, B) = `sqrt(square +[(-7) + square]^2`
∴ d(A, B) = `sqrt(square)`
∴ d(A, B) = `square`
A circle drawn with origin as the centre passes through `(13/2, 0)`. The point which does not lie in the interior of the circle 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 y axis equidistant from B and C is ______.
