Download Coordinate Geometry Assignment Key

Coordinate Geometry Assignment Key
Question #1 Prove that quadrilateral A(1,2), B(2,5), C(5,7) and D(4,4) is a parallelogram by using slopes. Slope formula: slope of slope of slope of slope of Parallel lines have equal slopes. ABCD is a parallelogram because it has two sets of parallel sides. QED. Question #2 Prove that A(1,1), B(4,4), C(6,2) are the vertices of a right triangle. Slope formula: slope of slope of Perpendicular lines have negative reciprocal slopes. Perpendicular lines meet to form right angles. So, is a right angle. is a right triangle since it contains a right angle. QED. Question #3 Prove that quadrilateral A(1,‐2), B(13,4), C(6,8) and D(‐2,4) is a trapezoid, but is NOT an isosceles trapezoid. Slope formula: slope of slope of slope of slope of Parallel lines have equal slopes. ABCD is a trapezoid because it has only one set of parallel sides. Distance Formula: ABCD is not an isosceles trapezoid because the legs are not of equal length. Question #4 Midpoint Formula midpoint of midpoint of A segment bisector intersects a segment at its midpoint. Since each diagonal has the same midpoint, they bisect each other. ABCD is a parallelogram because the diagonals bisect each other. Question #5 Prove that A(‐3,2), B(‐2,6), C(2,7) and D(1,3) is a rhombus. Distance Formula AB = CD = BC = AD making the opposite sides congruent as well as all sides congruent. ABCD is a parallelogram because its opposite sides are congruent. ABCD is a rhombus because it is a parallelogram with all sides congruent. Question #6 Prove that A(4,‐1), B(5,6), C(1,3) is an isosceles right triangle. Distance Formula is isosceles because it has two congruent sides.
This is an isosceles right triangle because it is both an isosceles triangle and a right triangle. is a right triangle because its sides satisfy the Pythagorean theorem. Question #7 Guinevere and Lancelot see a drawing of quadrilateral ABCD, A(2,2), B(5,‐2), C(9,1) and D(6,5). Guinevere says the figure is a rhombus, but not a square. Lancelot says the figure is a square. Write a proof to show who is making the correct observation. Distance Formula ABCD is a parallelogram because it has two sets of opposite sides congruent. ABCD is a rhombus because it is a parallelogram with 4 congruent sides. Slope Formula slope of slope of = = since the slopes are negative reciprocals. ABCD is a square because it is a parallelogram with a right angle and all sides are congruent. Lancelot is correct! So,