Coordinate Geometry with Triangles and Quadrilaterals

Quadrilateral ABCD is shown on the grid. Jonah finds the length of the sides of the quadrilateral before finding the perimeter. Which statement is true about the length of the sides of quadrilateral ABCD?

• Side DA has a length of 5 units.

• Side AB has a length of 6 units.

Jerome found the lengths of each side of triangle QRS as shown, but did not simplify his answers. Simplify the lengths of each side to answer the question. Which statement about triangle QRS is true?

• Triangle QRS is an equilateral triangle because QR = RS.

• Triangle QRS is an isosceles triangle because QR = QS.

• Triangle QRS is a scalene triangle because all sides have different lengths.

• Triangle QRS is an isosceles triangle because QR = RS.

Point A has an x coordinate of −2 and lies in a circle with a center at (0, 0) and a radius of 5. To the nearest tenth, what is the y-coordinate for point A?

• 4.5

• 4.6

• 4.7

• 4.8

Point A has an x-coordinate of 7 and lies below the x-axis on a circle with a center at (0, 0) and a radius of 8. To the nearest tenth, what is the y-coordinate for point A?

• -4.0

• -3.9

• -3.8

• -3.7

HIJK is a parallelogram because the midpoint of both diagonals is __________, which means the diagonals bisect each other.

• (1, -1)

• (1, 1)

• (1, 0)

• (0, 1)

Which statement proves that PQRS is a parallelogram?

• The midpoint of RP is (4, 5 1/2) and the slope of RP is -9/2.

• The midpoint of SQ is (4, 5 1/2) and SQ = 5.

What is the perimeter of kite KLMN?

What is the perimeter of parallelogram WXYZ?

• 16 units

• 22 units

What is the perimeter of square ABCD?

• 28 units

• 37 units