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प्रश्न
What point on the x-axis is equidistant from the points (7, 6) and (-3, 4)?
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उत्तर
Let the co-ordinates of the required point on x-axis be P (x, 0).
The given points are A (7, 6) and B (-3, 4).
Given, PA = PB
PA2 = PB2
(x - 7)2 + (0 - 6)2 = (x + 3)2 + (0 - 4)2
x2 + 49 - 14x + 36 = x2 + 9 + 6x + 16
60 = 20x
x = 3
Thus, the required point is (3, 0).
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संबंधित प्रश्न
Find the distance between the following pairs of points:
(2, 3), (4, 1)
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
Find the distance of the following point from the origin :
(13 , 0)
Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.
Show that the points (2, 0), (–2, 0), and (0, 2) are the vertices of a triangle. Also, a state with the reason for the type of triangle.
The points A (3, 0), B (a, -2) and C (4, -1) are the vertices of triangle ABC right angled at vertex A. Find the value of a.
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______.
Find distance between point Q(3, –7) and point R(3, 3)
Solution: Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = –7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `sqrt(square - 100)`
∴ d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `square`
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In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.
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Based on the above information answer the following questions using the coordinate geometry.
- Find the distance between Lucknow (L) to Bhuj (B).
- If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
- Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
[OR]
Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).
