Question

To find the midpoint of line segment AB, Fernando calculated 6.4 + (-2.5) = 3.9. What should his next step be?
A. Fernando has already made a mistake. He should have subtracted the x-values to get 8.9.
B. Fernando has already made a mistake. He should have calculated 6.4 + 2.5 = 8.9.
C. Fernando should divide 3.9 by 2, then repeat both steps using the y-values
D. Fernando should subtract the y-values

Answer 1

The calculation that Fernando performed seems to be relating to finding the midpoint of a line segment with endpoints \(A(x_1, y_1)\) and \(B(x_2, y_2)\). The midpoint formula is:

\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Given that Fernando calculated \(6.4 + (-2.5)\), he is likely working on the x-coordinates. Let's break down the options:

A. Incorrect. Fernando's addition was not supposed to involve a subtraction of x-values; the operation he performed was correct in the context of adding x-coordinates.

B. Incorrect. Fernando's initial step of adding \(6.4 + (-2.5)\) is valid as it implies he's dealing with \(6.4\) and \(-2.5\). He does not need to change it to \(6.4 + 2.5\).

C. This option is correct. After calculating \(6.4 + (-2.5) = 3.9\), Fernando should divide that sum by 2 to find the x-coordinate of the midpoint. He should then perform a similar calculation for the y-values.

D. Incorrect. While he could be subtracting y-values in a different context, in the context of finding the midpoint, he needs to add both x-values and y-values first and then divide by 2.

Therefore, the best next step for Fernando is:

**C. Fernando should divide 3.9 by 2, then repeat both steps using the y-values.**