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Find distance between point A(–1, 1) and point B(5, –7): Solution: Suppose A(x_1, y_1) and B(x_2, y_2) x_1 = –1, y_1 = 1 and x_2 = 5, y_2 = –7 Using distance formula

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प्रश्न

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`

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योग
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उत्तर

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) = \[\sqrt{\boxed{[5 - (-1)]^2} + [(-7) + \boxed{-1}]^2}\]

∴ d(A, B) = `sqrt(6^2 + (-8)^2`

∴ d(A, B) = `sqrt(36 + 64)`

∴ d(A, B) = \[\sqrt{\boxed{100}}\]

∴ d(A, B) = \[\boxed{10 \phantom{.}\text{units}}\]

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अध्याय 5: Co-ordinate Geometry - Q.2 (A)

संबंधित प्रश्न

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.

Using distance formula, find which of them is correct.


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

(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)


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


Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.


Distance of point (−3, 4) from the origin is ______.


Find the distance of the following point from the origin :

(5 , 12)


Find the coordinate of O , the centre of a circle passing through P (3 , 0), Q (2 , `sqrt 5`) and R (`-2 sqrt 2` , -1). Also find its radius.


Prove that the points (6 , -1) , (5 , 8) and (1 , 3) are the vertices of an isosceles triangle.


Prove that the points (7 , 10) , (-2 , 5) and (3 , -4) are vertices of an isosceles right angled triangle.


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


Find the distance of the following points from origin.
(a cos θ, a sin θ).


Calculate the distance between A (7, 3) and B on the x-axis, whose abscissa is 11.


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


The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.


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 ______.


∆ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to ∆DEF with vertices D(–4, 0), E(4, 0) and F(0, 4).


Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.


Show that points A(–1, –1), B(0, 1), C(1, 3) are collinear.


Read the following passage:

Alia and Shagun are friends living on the same street in Patel Nagar. Shagun's house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C.

Based on the above information, answer the following questions.

  1. How far is Alia's house from Shagun's house?
  2. How far is the library from Shagun's house?
  3. Show that for Shagun, school is farther compared to Alia's house and library.
    OR
    Show that Alia’s house, shagun’s house and library for an isosceles right triangle.

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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