Figures in the Coordinate Plane Answers

Mary thinks the triangle is equilateral. How would you support or dispute her conjecture?

1✔ –1undefined

equal✔ negative reciprocalsreciprocals

congruentparallel✔ perpendicular

parallel and share the same midpoint✔ perpendicular and share the same midpointthe same length

Prove the diagonals of the square with vertices P(0, 4), Q(4, 4), R(0, 0), and S(4, 0) are perpendicular bisectors of each other. Step 1: Calculate the slope of the diagonals.

Triangle ABC is an isosceles triangle in which sideAB = AC. What is the perimeter of triangle ABC?

Which steps will verify that a parallelogram is a rectangle? Check all that apply.Calculate the lengths of the diagonals, and show that they are equal.Calculate the lengths of all sides, and show that both pairs of opposite sides are congruent.Calculate the slope of each diagonal, and show that the lines are perpendicular.Calculate the midpoints of each diagonal, and show the diagonals bisect each other.Calculate the slopes of every side, and show that adjacent sides are perpendicular.

⇒ 20

Prove that the diagonals of kite UVWX are perpendicular. Step 1: Determine the slope of XV. The slope of XV is . Step 2: Determine the slope of UW. The slope of UW is . Step 3: The slopes of the diagonals are . The diagonals of kite UVWX are .

Which statement proves that quadrilateral HIJK is a kite?

2336✔ 4665

–10✔ 1

(0, 4) ✔ (2, 2)(4, 2)

(4, 0)✔ (2, 2)(2, 4)

Prove the diagonals of the square with vertices P(0, 4), Q(4, 4), R(0, 0), and S(4, 0) are perpendicular bisectors of each other. Step 1: Calculate the slope of the diagonals. The slope of diagonal PS is . The slope of diagonal QR is . Step 2: Calculate the midpoint of the diagonals. The midpoint of PS is . The midpoint of QR is . The diagonals of the square are perpendicular bisectors because the diagonals are .