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

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

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प्रश्न

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

बेरीज
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उत्तर

Let O(x1, y1) = O(0, 0) and B(x2, y2) = B(–5, 12)

∴ x1 = 0, y1 = 0, x2 = –5, y2 = 12

By distance formula,

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

= `sqrt((-5 - 0)^2 + (12 - 0)^2`

= `sqrt((-5)^2 + 12^2`

= `sqrt(25 + 144)`

= `sqrt(169)`

∴ d(O, B) = 13 units

∴ The distance between the points O and B is 13 units.

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पाठ 5: Co-ordinate Geometry - Exercise

संबंधित प्रश्‍न

If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.


If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y


The value of 'a' for which of the following points A(a, 3), B (2, 1) and C(5, a) a collinear. Hence find the equation of the line.


Find the distance between the following pair of points:

 (a + b, b + c) and (a – b, c – b)


Find the values of x, y if the distances of the point (x, y) from (-3, 0)  as well as from (3, 0) are 4.


Show that the points A (1, –2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.


Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.


A point P lies on the x-axis and another point Q lies on the y-axis.
Write the ordinate of point P.


Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.


The distances of point P (x, y) from the points A (1, - 3) and B (- 2, 2) are in the ratio 2: 3.
Show that: 5x2 + 5y2 - 34x + 70y + 58 = 0.


Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.


Find distance between point A(–3, 4) and origin O.


The distance between the points A(0, 6) and B(0, -2) is ______.


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 coordinates of the centroid of ΔEHJ are ______.


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 ______.


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If the point A(2, – 4) is equidistant from P(3, 8) and Q(–10, y), find the values of y. Also find distance PQ.


A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?


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