Question

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

You are given a line segment (AB) and a perpendicular line segment (CD).

Answer 1

Ill draw it out?

Answer 2

With coordinate geometry proofs, you need the coordinate plane.

Answer 3

That is what you are proving right?

Answer 4

In the triangle ADC and BDC, AD and BD are congruent because D is the midpoint of the segment AB. Also the side DC is common in both the triangles. This mean that angle CDA and angle CDB are both 90 degrees meaning they are congruent. This means the triangles are congruent because of the postulate Side-Angle-Side. So since the triangles are congruent, the distance from the two endpoints have to be equal.
^ that is what i said first but its wrong...

Answer 5

You need to label your drawing. Where are the points you are referring to?