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Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).
- a)(2, 3)
- b)(11,2)
- c)(0, 3)
- d)(1, 3)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Find the coordinates of the point equidistant from the points A(1, 2),...
Given three points A(1,2) B(3,-4) and C(5,-6)
we have to find the coordinates of the point equidistant from the points.
The point that is equidistant from three points is called circumcenter which can be evaluated to find the perpendicular bisectors.
To find the perpendicular bisectors of AB:
(11,2)
(11,2)Most Upvoted Answer
Find the coordinates of the point equidistant from the points A(1, 2),...
Given three points A(1,2) B(3,-4) and C(5,-6)
we have to find the coordinates of the point equidistant from the points.
The point that is equidistant from three points is called circumcenter which can be evaluated to find the perpendicular bisectors.
To find the perpendicular bisectors of AB:
(11,2)
(11,2)Free Test
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Community Answer
Find the coordinates of the point equidistant from the points A(1, 2),...
Solution:
Finding the midpoint of the line segment AB:
- The midpoint formula is:
- Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
- Midpoint of AB = ((1 + 3) / 2, (2 + (-4)) / 2)
= (2, -1)
Finding the midpoint of the line segment BC:
- Midpoint of BC = ((3 + 5) / 2, (-4 + (-6)) / 2)
= (4, -5)
Equidistant point from A, B, and C:
- The point equidistant from A, B, and C will be the midpoint of the line segment that connects the midpoints of AB and BC.
- Midpoint of the line segment connecting the midpoints of AB and BC = ((2 + 4) / 2, (-1 + (-5)) / 2)
= (3, -3)
Therefore, the coordinates of the point equidistant from A(1, 2), B(3, -4), and C(5, -6) is (3, -3), which corresponds to option B.
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