हिंदी

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

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प्रश्न

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

विकल्प

  • 7

  • 1

  • 5

  • 4

MCQ
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उत्तर

Distance of point (−3, 4) from the origin is 5.

Explanation:

Using the formula,

Distance = `sqrt(x^2 + y^2)`

= `sqrt((-3)^2 + 4^2)`

= `sqrt(9 + 16) = sqrt25 = 5`

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2018-2019 (March) Balbharati Model Question Paper Set 3

संबंधित प्रश्न

Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area


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.


Find the distance between the points:

A(1, –3) and B(4, –6)


Find the distance between the following pair of points.

L(5, –8), M(–7, –3)


Determine whether the points are collinear.

A(1, −3), B(2, −5), C(−4, 7)


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

2AB is equal to


Find the distance of the following point from the origin :

(5 , 12)


Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.


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


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


Calculate the distance between A (5, -3) and B on the y-axis whose ordinate is 9.


By using the distance formula prove that each of the following sets of points are the vertices of a right angled triangle.
(i) (6, 2), (3, -1) and (- 2, 4)
(ii) (-2, 2), (8, -2) and (-4, -3).


Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.


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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Case Study

Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites.
A guard, stationed at the top of a 240 m tower, observed an unidentified boat coming towards it. A clinometer or inclinometer is an instrument used for measuring angles or slopes(tilt). The guard used the clinometer to measure the angle of depression of the boat coming towards the lighthouse and found it to be 30°.

  1. Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
  2. After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?

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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