Geometry and the Coordinate Plane: math practice, Grade 5 – download the PDF

1 Axes and origin ★★★

Answer the questions about the coordinate plane.

1. Which axis is horizontal? Which axis is vertical?
2. What are the coordinates of the origin?
3. Which number of an ordered pair comes first, the move right or the move up?

2 Same numbers, different points ★★★

Describe how to reach the points \((6, 2)\) and \((2, 6)\) starting at the origin. Are they the same point?

3 Reading ordered pairs ★★★

Write the ordered pair for each point.

4 True or false? ★★★

Say whether each sentence is true or false. Explain your answer.

1. A point on the x-axis has a second coordinate of 0.
2. The point \((0, 5)\) is on the x-axis.
3. The first number of an ordered pair tells how far to go up.
4. The origin is where the two axes cross.

5 Name that quadrilateral ★★★

Name each quadrilateral.

1. It has 2 pairs of parallel sides, no right angles, and its sides are not all equal.
2. It has 4 right angles, and its neighboring sides have different lengths.
3. It has exactly one pair of parallel sides.

6 Triangles by their sides ★★★

Name each triangle by its sides.

1. 6 cm, 6 cm, 6 cm
2. 7 in, 7 in, 4 in
3. 5 cm, 6 cm, 9 cm

7 Parallel or perpendicular? ★★★

Say whether each pair of real-life lines is parallel or perpendicular.

1. The two rails of a straight train track.
2. A wall and the floor at the corner of a room.
3. The two long edges of a ruler.
4. The hands of a clock at 3:00.

8 Distances on the grid ★★★

On a coordinate plane, plot \(P(2, 1)\), \(Q(2, 6)\) and \(R(7, 1)\).

1. How long is the segment PQ? Is it horizontal or vertical?
2. How long is the segment PR?
3. Are PQ and PR parallel or perpendicular?

9 Which quadrilateral is PQRS? ★★★

Look at the figure.

1. Write the coordinates of P, Q, R and S.
2. How long are the horizontal sides?
3. Is PQRS a parallelogram? Is it a rectangle? Explain.

10 The bike courier ★★★

A courier rides from the bakery at \((1, 2)\) to the school at \((1, 8)\), and then to the library at \((5, 8)\). Each grid unit is half a mile.

1. How many units does the courier ride on each part?
2. How many miles is the whole ride?
3. Are the two parts parallel or perpendicular?

11 Always, sometimes or never? ★★★

Write always, sometimes or never.

1. A square is a rectangle.
2. A rectangle is a square.
3. A rhombus has 4 right angles.
4. A triangle has parallel sides.

12 Triangles by their angles ★★★

Name each triangle by its angles.

1. 40°, 60°, 80°
2. 90°, 35°, 55°
3. 110°, 30°, 40°

13 Perimeters from attributes ★★★

1. A rhombus has a perimeter of 30 cm. How long is each side?
2. A rectangle has a perimeter of 26 in and a length of 8 in. What is its width?

14 Sorting in a Venn diagram ★★★

Circle A is “at least one pair of parallel sides”. Circle B is “at least one right angle”. Place each quadrilateral in A only, B only, both, or neither.

1. Square
2. Rhombus with no right angle
3. Right trapezoid (a trapezoid with a right angle)
4. Kite with no right angle and no parallel sides

15 Finish the square ★★★

Three corners of a square are \(A(2, 3)\), \(B(6, 3)\) and \(C(6, 7)\).

1. Find the fourth corner D.
2. A student says D is at \((2, 6)\). Explain the mistake.

16 Missing corner of a parallelogram ★★★

The points \(K(1, 1)\), \(L(4, 1)\) and \(M(6, 4)\) are three corners of the parallelogram KLMN. Find N.

17 Which statements are true? ★★★

Say whether each statement is true. If it is false, give a counterexample.

1. Every rhombus is a parallelogram.
2. Every parallelogram is a rectangle.
3. Every square is a rhombus.

Then list every name that fits a square.

18 The drone flight ★★★

A drone starts at \((2, 1)\). It flies 3 units right, then 4 units up, then 2 units left, then 1 unit down. Each unit is 20 meters.

1. Where does the drone finish?
2. How many meters did it fly in all?
3. Going back along grid lines only, what is the shortest distance to the start?

19 Right and isosceles ★★★

1. Draw a triangle on the coordinate plane with corners \((1, 1)\), \((5, 1)\) and \((1, 5)\). Name it by its sides and by its angles.
2. Can a triangle have two right angles? Explain, using parallel lines.

20 Triangle Venn diagram ★★★

Circle A is “at least two equal sides”. Circle B is “has a right angle”. Place each triangle.

1. Equilateral triangle
2. Right isosceles triangle
3. Right scalene triangle
4. Obtuse isosceles triangle
5. Acute scalene triangle
6. Obtuse scalene triangle

21 The flower bed ★★★

Zoe marks a flower bed with corners \((1, 1)\), \((7, 1)\), \((5, 4)\) and \((3, 4)\). Each unit is 1.5 meters.

1. Which quadrilateral is it? How many pairs of parallel sides does it have?
2. How long are the two parallel sides in meters?
3. She puts a fence on the two parallel sides only. How many meters of fence does she need?