Prove using coordinate geometry: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpo

Question

attashe74 [19]

3 years ago

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Prove using coordinate geometry: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpo

ints of the segment.

Mathematics

1 answer:

frez [133] · Answer 1 · 2022-08-11T08:30:46+03:00

Let be A(2,2) and B(4, 4) two points, let be C the point which is on the perpendicular bisector of the segment AB, so the coordinate of C must be
C(2+4 / 2, 2 + 4 /2) = C(3,3)
<span>C is equidistant from the endpoints of the segment.
proof
vect AC= (1, 1), and vect CB= (1, 1), the length of each vect is
CB= sqrt2, and AC=</span>sqrt2, so it is prooved that AC=CB, C is equidistant to the two endpoints