In this lesson, students explore ways to find vertical and horizontal distances in the coordinate plane. In the first activity, students use repeated reasoning to explore the relationship between points with opposite coordinates (MP8). In the second activity, students develop strategies for finding the distance between two points where the coordinates might not be integers. Students can use previous strategies, such as considering the distance of a point from zero, or counting squares. Students will use these skills in Grade 7 to find distances on maps. In Grade 8, they will use these skills to draw slope triangles in the coordinate plane and find the lengths of their sides when considering graphs of proportional and non-proportional relationships.
- Compare and contrast (orally and in writing) the coordinates for points in different locations on the coordinate plane.
- Determine the vertical or horizontal distance between two points on the coordinate plane that share the same $x$- or $y$-coordinate.
- Generalize (orally) about the coordinates of points that are reflected across the $x$- or $y$-axis.
Let’s explore distance on the coordinate plane.
It may be useful, but not required, to provide access to tracing paper or rulers to help students think through the misconception that the length of a diagonal is equal to the length of a related horizontal or vertical distance in the coordinate plane.
- I can find horizontal and vertical distances between points on the coordinate plane.
The coordinate plane is divided into 4 regions called quadrants. The quadrants are numbered using Roman numerals, starting in the top right corner.