English

Calculate the Distance Between a (7, 3) and B on the X-axis Whose Abscissa is 11. - Mathematics

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

We know that any point on x-axis has coordinates of the form (x, 0).
Abscissa of point B = 11
Since, B lies of x-axis, so its co-ordinates are (11, 0).
AB = `sqrt((11 -7)^2 + (0 -3)^2)`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5 units

shaalaa.com
  Is there an error in this question or solution?
Chapter 28: Distance Formula - Exercise 28 [Page 335]

APPEARS IN

Selina Concise Mathematics [English] Class 9 ICSE
Chapter 28 Distance Formula
Exercise 28 | Q 24 | Page 335

RELATED QUESTIONS

Find the distance between two points

(i) P(–6, 7) and Q(–1, –5)

(ii) R(a + b, a – b) and S(a – b, –a – b)

(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`


Prove that the following set of point is collinear :

(5 , 1),(3 , 2),(1 , 3)


Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.


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


Using distance formula decide whether the points (4, 3), (5, 1), and (1, 9) are collinear or not.


The coordinates of the point which is equidistant from the three vertices of the ΔAOB as shown in the figure 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 ______.


If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.


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?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×