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

Find the Distances Between the Following Point. A(A, 0), B(0, A)

Advertisements
Advertisements

प्रश्न

Find the distances between the following point.
A(a, 0), B(0, a)

थोडक्यात उत्तर
Advertisements

उत्तर

A(a, 0), B(0, a)

\[AB = \sqrt{\left( 0 - a \right)^2 + \left( a - 0 \right)^2}\]

\[ = \sqrt{a^2 + a^2}\]

\[ = \sqrt{2 a^2}\]

\[ = a\sqrt{2}\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Co-ordinate Geometry - Problem Set 5 [पृष्ठ १२२]

APPEARS IN

बालभारती Geometry Mathematics 2 [English] Standard 10 Maharashtra State Board
पाठ 5 Co-ordinate Geometry
Problem Set 5 | Q 6.1 | पृष्ठ १२२

संबंधित प्रश्‍न

The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.

 


Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.


If P and Q are two points whose coordinates are (at2 ,2at) and (a/t2 , 2a/t) respectively and S is the point (a, 0). Show that `\frac{1}{SP}+\frac{1}{SQ}` is independent of t.


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


Prove that the points A(1, 7), B (4, 2), C(−1, −1) D (−4, 4) are the vertices of a square.


Find the distance between the points

A(1,-3) and B(4,-6)


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


Find the distance between the following pair of point in the coordinate plane.

(1 , 3) and (3 , 9)


Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).


x (1,2),Y (3, -4) and z (5,-6) are the vertices of a triangle . Find the circumcentre and the circumradius of the triangle.


Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).


A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a.


Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.


Given A = (3, 1) and B = (0, y - 1). Find y if AB = 5.


Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).


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


Show that the point (11, –2) is equidistant from (4, –3) and (6, 3).


The distance of the point P(–6, 8) from the origin is ______.


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×