This worksheet has 10 problems on the four-quadrant coordinate plane, aligned to Common Core 6.NS.C.6b, 6.NS.C.6c, 6.NS.C.8, and 6.G.A.3. Problems 1 to 7 cover quadrants, plotting, reflections, and distances between points.
Problems 8 to 10 draw polygons and solve map problems with several steps. Use absolute value to find each distance.
Problem 1: Name the quadrant
Name the quadrant of each point. If a point is on an axis, name the axis.
- \((3, 5)\)
- \((-2, 4)\)
- \((-6, -1)\)
- \((7, -3)\)
- \((0, -4)\)
Problem 2: Plot the points
Plot and label these points on the coordinate plane: \(A(2, 3)\), \(B(-4, 1)\), \(C(-3, -5)\), and \(D(5, -2)\).
Problem 3: Read ordered pairs
Write the ordered pair for each labeled point shown on the coordinate plane.
Problem 4: Reflect a point
The point \(A(5, -2)\) is shown. Write the coordinates of its reflection across each line.
- The x-axis
- The y-axis
- The x-axis, then the y-axis
Problem 5: Points that mirror each other
Points \(A(-6, 4)\) and \(B(6, 4)\) are shown. Describe how the coordinates of A and B are related, name the axis that is the line of reflection, and find the distance from A to B.
Problem 6: Distance on a horizontal line
Find the distance between \((-7, 3)\) and \((2, 3)\).
Problem 7: Distance on a vertical line
Find each distance.
- \(C(4, -8)\) and \(D(4, -3)\)
- \(E(-2, 6)\) and \(F(-2, -5)\)
Problem 8: Draw a rectangle
Plot the points \((-3, 2)\), \((4, 2)\), \((4, -3)\), and \((-3, -3)\). Connect them in order to form a rectangle. Find the length of each side and the perimeter.
Problem 9: Walking route
On a town map, each unit is one city block. The library is at \((-4, 5)\), the school is at \((-4, -2)\), and the park is at \((5, -2)\). Priya walks from the library to the school, and then to the park. Find the distance of each part and the total distance.
Problem 10: Triangle and its reflection
Triangle \(ABC\) has vertices \(A(-2, -1)\), \(B(5, -1)\), and \(C(5, 4)\).
- Find the lengths of sides \(AB\) and \(BC\).
- Reflect the triangle across the x-axis. Write the coordinates of \(A^{\prime}\), \(B^{\prime}\), and \(C^{\prime}\).
- Find the lengths of \(A^{\prime}B^{\prime}\) and \(B^{\prime}C^{\prime}\), and compare them with part a.
See every chapter on the Grade 6 math page.