Advertisements
Advertisements
प्रश्न
Find distance of point A(6, 8) from origin.
Advertisements
उत्तर
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
∴ The distance of point A(6, 8) from origin is 10 units.
APPEARS IN
संबंधित प्रश्न
If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.
If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.
Find the co-ordinates of points of trisection of the line segment joining the point (6, –9) and the origin.
Find the distance between the points
A(-6,-4) and B(9,-12)
Find the distance of the following points from the origin:
(ii) B(-5,5)
Using the distance formula, show that the given points are collinear:
(-1, -1), (2, 3) and (8, 11)
Find the distance between the following pairs of point in the coordinate plane :
(7 , -7) and (2 , 5)
Prove that the points (5 , 3) , (1 , 2), (2 , -2) and (6 ,-1) are the vertices of a square.
Find the distance between the origin and the point:
(-8, 6)
A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.
Points A (-3, -2), B (-6, a), C (-3, -4) and D (0, -1) are the vertices of quadrilateral ABCD; find a if 'a' is negative and AB = CD.
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.
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x = ______.
Find distance between point A(7, 5) and B(2, 5).
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
If the point A(2, – 4) is equidistant from P(3, 8) and Q(–10, y), find the values of y. Also find distance PQ.
What is the distance of the point (– 5, 4) from the origin?
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.
- How far is Alia's house from Shagun's house?
- How far is the library from Shagun's house?
- 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.
The distance of the point (5, 0) from the origin is ______.
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
