English
Maharashtra State BoardSSC (English Medium) 10th Standard

Find distance of point A(6, 8) from origin - Geometry Mathematics 2

Advertisements
Advertisements

Question

Find distance of point A(6, 8) from origin

Sum
Advertisements

Solution

Let A(x1, y1) = A(6, 8), O(x2, y2) = O(0, 0)

∴ x1 = 6, y1 = 8, x2 = 0, y2 = 0

By distance formula,

d(A, O) =`sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

= `sqrt((0 - 6)^2 + (0 - 8)^2`

= `sqrt(36 + 64)`

= `sqrt(100)`

= 10 cm

∴ The distance of point A(6, 8) from origin is 10 cm.

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Co-ordinate Geometry - Q.1 (B)

APPEARS IN

RELATED QUESTIONS

Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.


Find the values of x, y if the distances of the point (x, y) from (-3, 0)  as well as from (3, 0) are 4.


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 points

P(a sin ∝,a cos ∝ )and Q( acos ∝ ,- asin ∝)

 


Find the distance of  the following points from the origin:

(iii) C (-4,-6)


Find the distance between the following pairs of point.

W `((- 7)/2 , 4)`, X (11, 4)


Find the distance of the following point from the origin :

(5 , 12)


Prove that the following set of point is collinear :

(4, -5),(1 , 1),(-2 , 7)


Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius. 


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


Prove that the points (a, b), (a + 3, b + 4), (a − 1, b + 7) and (a − 4, b + 3) are the vertices of a parallelogram. 


From the given number line, find d(A, B):


The distances of point P (x, y) from the points A (1, - 3) and B (- 2, 2) are in the ratio 2: 3.
Show that: 5x2 + 5y2 - 34x + 70y + 58 = 0.


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


Show that the point (0, 9) is equidistant from the points (– 4, 1) and (4, 1)


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


Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?


If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.


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.

Show that Alia's house, Shagun's house and library for an isosceles right triangle.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×