Figures in the Coordinate Plane — Quiz

Question 16 • MASTER COURSE Geometry

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

Answer

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 .

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 .

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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