मराठी

If a and B Are the Points (−6, 7) and (−1, −5) Respectively, Then the Distance 2ab is Equal to - Mathematics

Advertisements
Advertisements

प्रश्न

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

2AB is equal to

पर्याय

  • A. 13

  • B. 26

  • C. 169

  • D. 238

MCQ
Advertisements

उत्तर

The given points are A (−6, 7) and B (−1, −5).

`therefore AB=sqrt((-6-(-1))^2+(7-(-5))2)`

`=sqrt((-6+1)^2+(7+5)^2)`

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

`=sqrt(25+144)`

`=sqrt169`

`=13`

`therefore 2AB=2xx13=26`

Thus, the distance 2AB is 26 units.

The correct answer is B.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2010-2011 (March) All india set 1

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius.


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.


A(–8, 0), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5. Show that : PQ = `3/8` BC.


Find the distance between the following pair of point.

T(–3, 6), R(9, –10)


Prove that the points (1 ,1),(-4 , 4) and (4 , 6) are the certices of an isosceles triangle.


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 centre of a circle is (2x - 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 unit.


Show that A(1, 2), (1, 6), C(1 + 2 `sqrt(3)`, 4) are vertices of a equilateral triangle


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:

If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.


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?

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×