Find the midpoint of (2, 4) and (8, 10).
Incorrect answer: (6, 6)
Do not average an x-coordinate with a y-coordinate. Also, adding horizontal and vertical distances gives a route along two sides, not the straight-line distance.
Confusing the midpoint and the distance
A midpoint averages coordinates. A distance measures a length and uses both coordinate differences.
The correction
(5, 7)
Average each coordinate: 10/2 = 5 and 14/2 = 7.
- Find horizontal and vertical differences between the points.
- For distance, square both differences, add, and take the square root.
- For midpoint, average the x-coordinates and separately average the y-coordinates.
Try the reasoning in another example
Find the midpoint of (−2, 5) and (4, 1).
- Average x: (−2 + 4)/2 = 1.
- Average y: (5 + 1)/2 = 3.
Answer: (1, 3)
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
The short check below reuses the first example as a retrieval question and adds a second question. It checks this method; it does not establish a grade level.
Your next step
2 questions · No time limitCheck this step for yourself
Choose an answer or enter it as shown. You can include units. Select “Not sure yet” to mark a skill for practice. Results stay on this page unless you download them.