Advertisements
Advertisements
Question
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?
Advertisements
Solution
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
RELATED QUESTIONS
If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
Find the distance between the following pairs of points:
(a, b), (−a, −b)
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 a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (−3, 4).
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Using the distance formula, show that the given points are collinear:
(-2, 5), (0,1) and (2, -3)
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
ABCD is a square . If the coordinates of A and C are (5 , 4) and (-1 , 6) ; find the coordinates of B and D.
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.
KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
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 ______.
Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
The coordinates of the centroid of ΔEHJ are ______.
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
The point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5).
Show that points A(–1, –1), B(0, 1), C(1, 3) are collinear.
