Question

describe and correct the error a student made in finding the mid - point of cd with c(-4,5) and d(-1,-4).
choose the correct answer below.
a. the student did not divide the numerator and denominator by 2 when calculating the mid - point.
b. the student used incorrect coordinates when calculating the mid - point.
c. the student swapped the x - and y - values when calculating the mid - point.
d. the student did not add the x - and y - coordinates when calculating the mid - point.
the correct answer is
(type an ordered pair, using integers or fractions.)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $C(-4,5)$ and $D(-1,-4)$, the correct calculation for the x - coordinate of the mid - point is $\frac{-4+( - 1)}{2}=\frac{-4 - 1}{2}=-\frac{5}{2}$, and for the y - coordinate is $\frac{5+( - 4)}{2}=\frac{5 - 4}{2}=\frac{1}{2}$.

Step2: Analyze student's work

The student's work shows incorrect operations. The student did not add the x - coordinates ($-4$ and $-1$) and y - coordinates ($5$ and $-4$) as required by the mid - point formula.

Answer:

D. The student did not add the x - and y - coordinates when calculating the midpoint.
$(-\frac{5}{2},\frac{1}{2})$