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प्रश्न
Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).
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उत्तर
Since the point is on the y-axis so, X-coordinate is zero.
Let the point be (0, y)
Its distance from (5, –2) and (–3, 2) are equal
∴ `sqrt((0 -5)^2 + (y+2)^2) = sqrt((0+3)^2 + (y -2)^2)`
⇒ `25 + y^2 + 4y + 4 = 9 + y^2 - 4y + 4 ....["squaring both sides"]`
⇒ `4y + 29 = -4y + 13`
⇒ `4y + 4y = 13 - 29`
⇒`8y = (-16)/(8) = -2`
Thus, the point is (0,-2)
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).
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0)
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.
Show that the points A (1, 0), B (5, 3), C (2, 7) and D (−2, 4) are the vertices of a parallelogram.
Show that the following points are the vertices of a rectangle
A (0,-4), B(6,2), C(3,5) and D(-3,-1)
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
In the above figure, seg PA, seg QB and RC are perpendicular to seg AC. From the information given in the figure, prove that: `1/x + 1/y = 1/z`
Point (–3, 5) lies in the ______.
Point (0, –7) lies ______.
