Question

CD is a perpendicular bisector of AB, where D is on AB. The Perpendicular Bisector Theorem states that AC=BC. How would the result change if point C were reflected across AB?

A) AC > BC
B) AC ≠ BC
C) There would be no changes
D) AC < BC

Answer 1

Reflecting point C across the line AB would not change the distances AC and BC because the reflection preserves equidistance from points A and B; hence, the distances remain equal.

Step-by-step explanation:

If CD is a perpendicular bisector of AB, with D on AB, and C is reflected across AB, we must recognize that reflecting C across AB would create a point that is equidistant from A and B, just as the original point C was.

The reflection of a point across a line produces a mirror image of that point in relation to the line. Hence, the distances AC and BC remain equal, as the reflected point maintains the same distance to A and B as the original point C did. Therefore, the correct answer is C) There would be no changes.