To find the midpoint of the line segment AB, Fernando calculated 6.4+(-2.5)=3.9. What should his next step be?

Question

A. Fernando has already made a mistake. He should have calculated 6.4+2.5=8.9
B. Fernando should subtract the y-values
C. Fernando should divide 3.9 by 2, then repeat both steps using the y-values
D. Fernando has already made a mistake. He should have subtracted the x-values to get 8.9

Answer 1

To find the midpoint of a line segment defined by two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), the formula is:

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

In Fernando's calculation, he appears to be adding \( 6.4 \) and \( -2.5 \), which could imply that \( 6.4 \) is one x-value and \( -2.5 \) is another x-value.

1. If he is indeed using the x-values of points A and B:

   • He should add \( 6.4 + (-2.5) \) to find the sum of the x-coordinates, which is \( 3.9 \).
   • The next step would be to divide this sum by 2 to find the average (midpoint).

2. If he mistakenly thinks he is finding the midpoint using incorrect values:

   • The result \( 6.4 + 2.5 = 8.9 \) suggests he may have misinterpreted the values, as it would not represent a correct calculation for finding the midpoint.

Based on this logic, the best option is:

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