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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?
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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.
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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. |
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OR
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