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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

Find distance of point A(6, 8) from origin.

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प्रश्न

Find distance of point A(6, 8) from origin.

बेरीज
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उत्तर

Let A(x1, y1) = A(6, 8), O(x2, y2) = O(0, 0)

∴ x1 = 6, y1 = 8, x2 = 0, y2 = 0

By distance formula,

d(A, O) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

= `sqrt((0 - 6)^2 + (0 - 8)^2`

= `sqrt(36 + 64)`

= `sqrt(100)`

= 10

∴ The distance of point A(6, 8) from origin is 10 units.

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पाठ 5: Co-ordinate Geometry - Exercise

संबंधित प्रश्‍न

Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.


Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:

 (−3, 5), (3, 1), (0, 3), (−1, −4)


If a ≠ b ≠ 0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.


Find the distance of a point P(x, y) from the origin.


Find the distance between the points:

A(1, –3) and B(4, –6)


If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance

2AB is equal to


The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.


Find the distance between the following pair of point in the coordinate plane :

(5 , -2) and (1 , 5)


Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).


Prove that the points (1 , 1) , (-1 , -1) and (`- sqrt 3 , sqrt 3`) are the vertices of an equilateral triangle.


ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.


The distance between the points (3, 1) and (0, x) is 5. Find x.


Prove that the points P (0, -4), Q (6, 2), R (3, 5) and S (-3, -1) are the vertices of a rectangle PQRS.


Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.


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.


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).


Find distance between points O(0, 0) and B(–5, 12).


Find distance CD where C(–3a, a), D(a, –2a).


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 coordinates of the centroid of ΔEHJ are ______.


Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?


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