# 2.1: Midpoints in the Coordinate Plane

**At Grade**Created by: CK-12

*This activity is intended to supplement Geometry, Chapter 1, Lesson 4.*

**ID: 8614**

## Problem 1 – Midpoints of Horizontal or Vertical Segments

**Step 1:**

- Open a new Cabri Jr. file. If the axes are not currently showing, they should select
**Hide/Show**>**Axes.** - Construct a horizontal segment in the first quadrant using the
**Segment**tool.

**Step 2:**

- Select
**Coord. & Eq.**and show the coordinates for the endpoints of the segment.

If the coordinates of the endpoints are not integers, they need to use the **Hand** tool to drag the endpoints until the coordinates are integers.

**Step 3:**

- Make a prediction about the coordinates for the midpoint of the segment.
- To check your predictions, select
**Midpoint**, construct the midpoint of the segment, and then show its coordinates.

**Step 4:**

- Before moving on, hide the coordinates of the midpoint with the
**Hide/Show**>**Object**tool. - Use the
**Hand**tool to drag the segment to another location. If you drag the entire segment, it will remain horizontal.

Make a prediction about the new coordinates of the midpoint and check your prediction by showing the coordinates of the midpoint.

**Step 5:**

- Repeat this exploration with a vertical segment.

## Problem 2 – Midpoints of Diagonal Segments

**Step 1:**

- Open a new Cabri Jr. file. If needed, select
**Hide/Show**>**Axes**to show the coordinate axes.

Use the **Segment** tool to construct a diagonal segment in the first quadrant.

**Step 2:**

- Select
**Coord. & Eq.**and show the coordinates for the endpoints of the segment.

- If the coordinates of the endpoints are not integers, use the
**Hand**tool to drag the endpoints to make the coordinates integers.

**Step 3:**

- Make a prediction about the coordinates for the midpoint of the segment.
- To check your prediction, construct the midpoint of the segment and show the coordinates of the midpoint.

**Step 4:**

- Hide the coordinates of the midpoint with the
**Hide/Show**>**Object**tool. - Using the
**Hand**Tool, drag the segment to another location. If the entire segment is selected, it will keep the same diagonal slant.

Make a prediction about the new coordinates of the midpoint and check their prediction by showing the coordinates of the midpoint.

**Step 5:**

- Repeat this exploration with a new segment.

**Step 6:** *Describe in words how to find the coordinates of the midpoint of a segment if you know the coordinates of the endpoints. Try to write a formula or a rule for midpoints.*