# Lesson 13

Distances and Shapes on the Coordinate Plane

### Lesson Narrative

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. They may also subtract corresponding coordinates to determine the distance. Students will use these skills next year to draw slope triangles in the coordinate plane and find the lengths of their sides when considering graphs of proportional and non-proportional relationships.

### Learning Goals

Teacher Facing

• 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.
• Draw a polygon in the coordinate plane given the coordinates for its vertices.

### Student Facing

Let’s explore distance on the coordinate plane.

### Required Preparation

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.

### Student Facing

• I can find horizontal and vertical distances between points on the coordinate plane.
• I can plot polygons on the coordinate plane when I have the coordinates for the vertices.

Building On