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) AC < BC
d) The result remains the same.

Answer 1

According to the Perpendicular Bisector Theorem, AC equals BC when CD is the perpendicular bisector of AB. If point C is reflected across AB, the lengths of AC and BC will no longer be equal.

Step-by-step explanation:

The subject matter involves using the Perpendicular Bisector Theorem to determine the equality of line segments in a geometric figure. According to the theorem, in triangle ABC, where CD is the perpendicular bisector of AB and D is the point where CD intersects AB, AC equals BC. However, if point C is reflected across AB, the symmetry of the figure changes and the lengths of AC and BC will no longer be equal. Without additional information, it is impossible to determine whether AC will be greater than or less than BC post reflection. The result that AC equals BC holds true only as long as point C remains on the perpendicular bisector of AB.