Figures in the Coordinate Plane — Quiz

Question 10 • MASTER COURSE Geometry

Which statement proves that the diagonals of square PQRS are perpendicular bisectors of each other?

Answer

The midpoint of both diagonals is open paren 4 and 1 half comma 5 and 1 half close paren , the slope of line segment RP is 7 , and the slope of line segment SQ is negative 1 seventh .

The length of line segment SQ and line segment RP are both square root of 50 .

The length of line segment SP , line segment PQ , line segment RQ , and line segment SR are each 5 .

The slope of line segment SP and line segment RQ is negative 4 thirds and the slope of line segment SR and line segment PQ is 3 fourths .

Explanation

To prove the diagonals are perpendicular bisectors of each other, show they share the same midpoint and are perpendicular. Choice A gives both diagonals the midpoint (4½, 5½), so they bisect each other. Their slopes are 7 and −1/7, which are negative reciprocals, so the diagonals are perpendicular. The other choices show equal diagonal lengths, equal side lengths, or parallel opposite sides, but do not establish both required facts.

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