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The co-ordinates of the point on x-axis which is equidistant from the points (5, 4) and (– 2, 3) are :
  • a)
    (2, 0)
  • b)
    (3, 0)
  • c)
    (0, 2)
  • d)
    (0, 3).
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The co-ordinates of the point on x-axis which is equidistant from the ...
Let the point on x-axis be (a,0)
Since PA = PB  PA2 = PB2
 (a + 2)2 + (0 - 5)2 = (a - 2)2 + (0 + 3)2
 (a + 2)2 - (a - 2)2 = 9 - 25 = -16
 8a = -16  a = -2.
 The required point is (-2,0).
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Most Upvoted Answer
The co-ordinates of the point on x-axis which is equidistant from the ...
Approach:
To find the point on the x-axis equidistant from two given points, we need to find the midpoint of the line segment connecting the two points. The x-coordinate of this midpoint will be the required point on the x-axis.

Given points:
Point A (5, 4) and Point B (-2, 3)

Finding the midpoint:
- Midpoint formula: ((x1 + x2) / 2, (y1 + y2) / 2)
- Midpoint = ((5 + (-2)) / 2, (4 + 3) / 2)
- Midpoint = (3 / 2, 7 / 2)
- Midpoint = (1.5, 3.5)

Equidistant point on the x-axis:
Since the point lies on the x-axis, the y-coordinate will be 0.
Therefore, the equidistant point on the x-axis is (1.5, 0), which can be simplified to (3/2, 0).

Conclusion:
The point on the x-axis equidistant from the points (5, 4) and (-2, 3) is (3/2, 0), which is option A.
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The co-ordinates of the point on x-axis which is equidistant from the points (5, 4) and (– 2, 3) are :a)(2, 0)b)(3, 0)c)(0, 2)d)(0, 3).Correct answer is option 'A'. Can you explain this answer?
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