Distance & Midpoint Worksheet
Goal: Find the distance between two points with the Pythagorean theorem, find midpoints by averaging coordinates, and spot horizontal and vertical segments.
What to do
- Open the distance, midpoint & slope tool.
- For each pair of points in the table, type the coordinates into “Point A · x”, “Point A · y”, “Point B · x” and “Point B · y”, or drag the points on the grid. Record the distance, midpoint and slope.
- For each row, sketch the right triangle whose legs are Δx and Δy.
Record your results
| Setting | Distance | Midpoint | Slope |
|---|---|---|---|
| A(0, 0), B(3, 4) | |||
| A(−3, −2), B(4, 5) | |||
| A(1, 2), B(7, 2) | |||
| A(2, −1), B(2, 5) | |||
| A(−4, 3), B(2, −5) |
Questions
For A(0, 0) and B(3, 4), use Δx, Δy and the Pythagorean theorem to find the distance.
Find the distance from A(−3, −2) to B(4, 5) by hand. Write it as a square root, then round.
How do you find a midpoint without the tool? Show it for A(−4, 3) and B(2, −5).
Two rows have a distance of 6. What is special about these pairs of points, and what are their slopes?
M(4, 2) is the midpoint of segment AB, and A is (1, 2). Find B.
Which pair of points is farthest apart? Show the distance calculation.
Free from Geometry Lab · geometrylab.net · 8.G.B.8: Apply the Pythagorean theorem to find the distance between two points in a coordinate system.
Teaching with this? Find the answer key and more activities on the Geometry Lab for teachers page.