Testinar Grade 6 math

Polygons on the Coordinate Plane

Students will build Grade 6 mastery of polygons on the coordinate plane using models, equations, and test-style reasoning.

CH04-04 Geometry

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A rectangle has vertices at \((1,1)\), \((7,1)\), \((7,4)\), and \((1,4)\). What is its perimeter?
1. \(9\) units
2. \(15\) units
3. \(18\) units
4. \(24\) units
A triangle has vertices at \((2,1)\), \((8,1)\), and \((5,5)\). What is the length of the base?
1. \(4\) units
2. \(6\) units
3. \(8\) units
4. \(10\) units
What type of polygon is shown?
1. Square
2. Pentagon
3. Trapezoid
4. Rectangle
A quadrilateral has vertices at \((1,2)\), \((4,2)\), \((5,6)\), and \((2,6)\). What is the length of the top side?
1. \(2\) units
2. \(3\) units
3. \(4\) units
4. \(5\) units
What is the perimeter of the rectangle shown above?
1. \(9\) units
2. \(12\) units
3. \(14\) units
4. \(16\) units
A rectangle has vertices at \((3,2)\), \((8,2)\), \((8,6)\), and \((3,6)\). If a point is at \((8,2)\), which vertex is diagonally opposite?
1. \((3,6)\)
2. \((3,2)\)
3. \((8,6)\)
4. \((8,2)\)
What is the length of side AB?
1. \(3\) units
2. \(4\) units
3. \(8\) units
4. \(6\) units
What is the length of a horizontal segment from \((2,4)\) to \((8,4)\)?
1. \(4\) units
2. \(5\) units
3. \(7\) units
4. \(6\) units

Teacher and parent reference

Answer key and explanations

C. \(18\) units
Length \(=7-1=6\) units; width \(=4-1=3\) units. Perimeter \(=2(6+3)=18\) units.
B. \(6\) units
The base goes from \((2,1)\) to \((8,1)\), which are both on the same horizontal line. The distance is \(8-2=6\) units.
D. Rectangle
The shape has four sides with opposite sides parallel and all angles at \(90\) degrees. It is a rectangle but not a square since length \(\neq\) width.
B. \(3\) units
The top side goes from \((2,6)\) to \((5,6)\), both at \(y=6\). Distance is \(5-2=3\) units.
C. \(14\) units
Width \(=5-1=4\) units; height \(=4-1=3\) units. Perimeter \(=2(4+3)=14\) units.
A. \((3,6)\)
Diagonal corners of a rectangle are \((3,2)\) with \((8,6)\), and \((8,2)\) with \((3,6)\). The diagonally opposite vertex to \((8,2)\) is \((3,6)\).
D. \(6\) units
Side AB is horizontal from \((1,2)\) to \((7,2)\). Length \(=7-1=6\) units.
D. \(6\) units
For a horizontal segment, subtract the \(x\)-coordinates: \(8-2=6\) units.