Advertisements
Advertisements
प्रश्न
Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?
उत्तर
Co-ordinates of A = (0, 2)
Co-ordinates of O = (0, 0)
Co-ordinates of B = (1, 2)
Distance between two points = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
By distance formula,
d(O, A) = `sqrt((0 - 0)^2 + (0 - 2)^2`
= `sqrt((0)^2 + (-2)^2`
= `sqrt(0 + 4)`
= 2 ......(i)
d(O, B) = `sqrt((0 - 1)^2 + (0 - 2)^2`
`sqrt((-1)^2 + (-2)^2`
= `sqrt(1 + 4)`
= `sqrt(5)` ......(ii)
∴ From (i) and (ii),
d(O, B) > d(O, A)
∴ d(O, B) > Radius of circle
∴ Point B(1, 2) does not lie on the circle but lies outside the circle.
APPEARS IN
संबंधित प्रश्न
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)
Find the distance of a point P(x, y) from the origin.
The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.
Find the distance of the following points from the origin:
(iii) C (-4,-6)
Using the distance formula, show that the given points are collinear:
(-2, 5), (0,1) and (2, -3)
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).
Find the distance between the origin and the point:
(8, -15)
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.
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
Calculate the distance between A (7, 3) and B on the x-axis, whose abscissa is 11.
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x
Show that P(– 2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle
Show that the points (2, 0), (– 2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason
The distance between the points (0, 5) and (–5, 0) is ______.
The distance of the point (α, β) from the origin is ______.
What is the distance of the point (– 5, 4) from the origin?
|
Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane. |
- At an instance, the midfielders and forward formed a parallelogram. Find the position of the central midfielder (D) if the position of other players who formed the parallelogram are :- A(1, 2), B(4, 3) and C(6, 6)
- Check if the Goal keeper G(–3, 5), Sweeper H(3, 1) and Wing-back K(0, 3) fall on a same straight line.
[or]
Check if the Full-back J(5, –3) and centre-back I(–4, 6) are equidistant from forward C(0, 1) and if C is the mid-point of IJ. - If Defensive midfielder A(1, 4), Attacking midfielder B(2, –3) and Striker E(a, b) lie on the same straight line and B is equidistant from A and E, find the position of E.
