Distance and Slope in Quadrilaterals on Coordinate Plane

You can prove both pairs of opposite sides are parallel by using the slope formula.

• True

• False

What formula would you use to show lengths are equal?

• Slope Formula

• Distance Formula

• Midpoint Formula

Prove that the quadrilateral with vertices at (2,3), (5,7), (8,5), and (5,1) is a parallelogram.

• Calculate the area of the quadrilateral and show that it is equal to zero.

• Calculate the slopes of the opposite sides and show that they are equal.

• Prove that the diagonals bisect each other.

• Show that the opposite angles are equal.

Prove that the quadrilateral with vertices at (1,2), (3,6), (7,6), and (5,2) is a rhombus using coordinate proofs.

• All four sides are congruent, so the quadrilateral is a rhombus.

• The opposite angles are equal, so it is a rhombus

• The diagonals are perpendicular, so it is a rhombus

• The sum of the interior angles is 360 degrees, so it is a rhombus

• Find the slope of 2 sides.

• Find the slope of all 4 sides.

• Find the slope of the diagonals.

• Find the length of all 4 sides.

Use slope and/or the distance formula to determine the most precise name for the figure: A(–6, –3), B(1, 0), C(4, 7), D(–3, 4).

• kite

• rectangle

• square

• rhombus

In order to prove this parallelogram is a RECTANGLE, we would have to show that...

• Adjacent sides have slopes that are OPPOSITE RECIPROCALS

• Adjacent sides have EQUAL slopes

• Opposite sides have EQUAL slopes

• Opposite sides have slopes that are OPPOSITE RECIPROCALS

Julia proved ABCD is a parallelogram. She notices that side AB has a slope of 8/3 and BC has a slope of 1/3. What can she classify ABCD as?

• A rectangle

• A square

• A rhombus

• Just a parallelogram

Use slope and/or the distance formula to determine the most precise name for the figure: A(–3, –5), B(4, –2), C(7, –9), D(0, –12).

• square

• rhombus

• trapezoid

• kite

Sarah proved that this is a square. The slopes of -2/5 and 5/2 made her able to do this. How come?

• Because those slopes form parallel lines.

• Because those slopes form perpendicular lines, creating right angles.

• Because those slopes make the sides congruent.