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प्रश्न
Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).
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उत्तर
Let P(x, 0) be the point on the x-axis.
Then as per the question we have
AP = 10
`\implies sqrt((x - 11)^2 + (0 + 8)^2` = 10
`\implies` (x – 11)2 + 82 = 100 ...(Squaring both sides)
`\implies` ( x – 11)2 = 100 – 64
`\implies` ( x – 11)2 = 36
`\implies` x – 11 = ±6
`\implies` x - 11 = 6 or x - 11 = -6
`\implies` x = 6 + 11 or x = -6 + 11
`\implies` x = 17 or x = 5
Hence, the points on the x-axis are (17, 0) and (5, 0).
संबंधित प्रश्न
(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
- how many cross - streets can be referred to as (4, 3).
- how many cross - streets can be referred to as (3, 4).
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by x-axis Also, find the coordinates of the point of division in each case.
Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).
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If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______.
The point at which the two coordinate axes meet is called the ______.
If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is ______.
The coordinates of a point whose ordinate is `-1/2` and abscissa is 1 are `-1/2, 1`.
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
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