You are the Grader!  This problem is worth 10 points.  How would you grade each of the answers below.

Problem:  Given a right triangle ABC, with A the right angle, let M be the midpoint of the hypotenuse BC.  Prove that the lengths MA = MB = MC.

Answer 1. Let MF be the perpendicular bisector of AB and let ME be the perpendicular bisector of AC.  Then by the locus property for perpendicular bisectors, MA = MB (since M is on the perpendicular bisector of AB) and MA = MC (since M is on the perpendicular bisector of AC).  Thus MB = MA = MC.  QED.

Answer 2.  Let MF be the perpendicular bisector of AB.  Then by the locus property for perpendicular bisectors, MA = MB.  Since M is the midpoint of BC, MB = MC.  Thus MB = MA = MC.  QED.

You are the Grader!  This problem is worth 10 points.  How would you grade each of the answers below.

Problem:  Given a right ABC, let M be the midpoint of the side BC. Prove that the lengths MA = MB = MC.

Answer 1. Let MF be the perpendicular bisector of AB and let ME be the perpendicular bisector of AC.  Then by the locus property for perpendicular bisectors, MA = MB (since M is on the perpendicular bisector of AB) and MA = MC (since M is on the perpendicular bisector of AC).  Thus MB = MA = MC.  QED.

Answer 2.  Let MF be the perpendicular bisector of AB.  Then by the locus property for perpendicular bisectors, MA = MB.  Since M is the midpoint of BC, MB = MC.  Thus MB = MA = MC.  QED.