Question

Yolanda calculated the midpoint of line segment
to be
. What mistake did she make?
Statement #1: Yolanda averaged the values from point
and then averaged the values from point
.
Statement #2: Yolanda forgot to divide the sums by 2.
Statement #3: Yolanda subtracted when she should have added.

explains Yolanda’s mistake

Answer 1

I don't have the endpoints or Yolanda's computed midpoint in the message, so I can't pick which specific statement is correct for this case. Give me the two endpoints or Yolanda's answer and I will tell you exactly which mistake she made.

Meanwhile, here's how you can tell which statement applies (let the endpoints be (x1,y1) and (x2,y2) and Yolanda's result be M' = (a,b)):

- If she averaged coordinates within each point (Statement 1): then
a = (x1 + y1)/2 and b = (x2 + y2)/2.
That is, each coordinate of M' equals the average of the coordinates of one endpoint.

- If she forgot to divide by 2 (Statement 2): then
a = x1 + x2 and b = y1 + y2.
In other words M' is twice the correct midpoint.

- If she subtracted when she should have added (Statement 3): then
a = (x1 − x2)/2 (or (x2 − x1)/2) and b = (y1 − y2)/2 (or (y2 − y1)/2).
So one or both coordinates of M' are halves of differences of the endpoint coordinates instead of halves of sums.

Give the endpoints or Yolanda's computed midpoint and I’ll identify which of these happened.