Exam: Geometry 04.01 Using the Coordinates

Quadrilateral ABCD has coordinates A (3, −5), B (5, −2), C (10, −4), D (8, −7). Quadrilateral ABCD is a

parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular

Connor is constructing square ABCD. He has plotted A at (−2, 4), C at (−1, 1) and D at (−3, 2). Which coordinate could be the location of point B?

(0, 3)

Connor is constructing parallelogram ABCD. He has plotted A at (−2, 4), B at (0, 3), and D at (−3, 2). Which coordinate could be the location of point C?

(−1, 1)

Which characteristics will prove that ΔDEF is a right, scalene triangle?

Line de , line ef , and df are all different lengths, and the slopes of and opposite reciprocals.

Ivan used coordinate geometry to prove that quadrilateral EFGH is a square. StatementReason1. Quadrilateral EFGH is at E (−2, 3), F (1, 6), G (4, 3), and H (1, 0)1. Given2.__?__2.E (−2, 3) F (1, 6)F (1, 6) G (4, 3)G (4, 3) H (1, 0)E (−2, 3) H (1, 0)3. 3. E (−2, 3) F (1, 6)G (4, 3) H (1, 0)4. __?__4. E(−2, 3) H (1, 0)F (1, 6) G (4, 3)5. and are perpendicular to 5. The slope of and is 1. The slope of is −1.6. __?__6. The slope of and is −1. The slope of is 1.7. Quadrilateral EFGH is a square7. All sides are congruent, opposite sides are parallel, and adjacent sides are perpendicular.

Line ef,fg ,gh , eh and are congruent

Lydia graphed ΔXYZ at the coordinates X (0, −4), Y (2, −3), and Z (2, −6). She thinks ΔXYZ is a right triangle. Is Lydia's assertion correct?

No; the slopes of line xy and xz are not opposite reciprocals.

Which statement explains how you could use coordinate geometry to prove the opposite sides of a quadrilateral are congruent?

Use the distance formula to prove the lengths of the opposite sides are the same.

How can you prove a triangle is isosceles?

Use the distance formula to see if at least two sides are congruent.

Which statement explains how you could use coordinate geometry to prove the diagonals of a quadrilateral are perpendicular?

Use the slope formula to prove the slopes of the diagonals are opposite reciprocals.

Which characteristics will prove that ΔDEF is an acute, isosceles triangle?

line df and ef are congruent to each other but not to , and their slopes are not related.

Quadrilateral ABCD has coordinates A (3, 5), B (5, 2), C (8, 4), D (6, 7). Quadrilateral ABCD is a

square, because all four sides are congruent and adjacent sides are perpendicular

ΔSTU is located at S (−3, 0), T (0, −3), and U (3, −3). Which statement correctly classifies ΔSTU?

ΔSTU is a scalene triangle.