Coordinate Plane — Practice Problems and Worked Solutions

The formulas you need here

16 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Where is the point located?

   $$(3,2)$$

   Answer: $\text{Quadrant I}$

   Step-by-step solution

   1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
   2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
   3. $$\text{Quadrant I}$$
2. 2.

   Where is the point located?

   $$(-4,1)$$

   Answer: $\text{Quadrant II}$

   Step-by-step solution

   1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
   2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
   3. $$\text{Quadrant II}$$
3. 3.

   Where is the point located?

   $$(-2,-5)$$

   Answer: $\text{Quadrant III}$

   Step-by-step solution

   1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
   2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
   3. $$\text{Quadrant III}$$
4. 4.

   Where is the point located?

   $$(3,-1)$$

   Answer: $\text{Quadrant IV}$

   Step-by-step solution

   1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
   2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
   3. $$\text{Quadrant IV}$$
5. 5.

   Where is the point located?

   $$(0,4)$$

   Answer: $y\text{-axis}$

   Step-by-step solution

   1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
   2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
   3. $$y\text{-axis}$$
6. 6.

   Where is the point located?

   $$(-5,0)$$

   Answer: $x\text{-axis}$

   Step-by-step solution

   1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
   2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
   3. $$x\text{-axis}$$
7. 7.

   Where is the point located?

   $$(6,1)$$

   Answer: $\text{Quadrant I}$

   Step-by-step solution

   1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
   2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
   3. $$\text{Quadrant I}$$
8. 8.

   Where is the point located?

   $$(-1,7)$$

   Answer: $\text{Quadrant II}$

   Step-by-step solution

   1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
   2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
   3. $$\text{Quadrant II}$$
9. 9.

   Where is the point located?

   $$(-3,-2)$$

   Answer: $\text{Quadrant III}$

   Step-by-step solution

   1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
   2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
   3. $$\text{Quadrant III}$$
10. 10.

    Where is the point located?

    $$(5,-4)$$

    Answer: $\text{Quadrant IV}$

    Step-by-step solution

    1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
    2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
    3. $$\text{Quadrant IV}$$
11. 11.

    Where is the point located?

    $$(0,-3)$$

    Answer: $y\text{-axis}$

    Step-by-step solution

    1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
    2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
    3. $$y\text{-axis}$$
12. 12.

    Where is the point located?

    $$(2,0)$$

    Answer: $x\text{-axis}$

    Step-by-step solution

    1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
    2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
    3. $$x\text{-axis}$$
13. 13.

    Where is the point located?

    $$(0,0)$$

    Answer: $\text{origin}$

    Step-by-step solution

    1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
    2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
    3. $$\text{origin}$$
14. 14.

    Where is the point located?

    $$(-8,3)$$

    Answer: $\text{Quadrant II}$

    Step-by-step solution

    1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
    2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
    3. $$\text{Quadrant II}$$
15. 15.

    Where is the point located?

    $$(4,9)$$

    Answer: $\text{Quadrant I}$

    Step-by-step solution

    1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
    2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
    3. $$\text{Quadrant I}$$
16. 16.

    Where is the point located?

    $$(-6,-6)$$

    Answer: $\text{Quadrant III}$

    Step-by-step solution

    1. $$\text{Read the point as }(x,y):\text{ horizontal first, vertical second.}$$
    2. $$\text{Use the signs of }x\text{ and }y\text{ to identify the location.}$$
    3. $$\text{Quadrant III}$$

More from Math Foundations

• Order of Operations
• Signed Numbers
• Fraction Sense
• Ratios and Percentages
• Exponents and Roots
• Algebraic Expressions
• Linear Equations
• Polynomial Basics
• Inequalities
• Reading Graphs
• Function Machines
• Substitution
• Factoring Basics