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2.1: Midpoints in the Coordinate Plane

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.

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TI.MAT.ENG.SE.1.Geometry.2.1

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