Question

describe and correct the error a student made in finding the midpoint of $overline{cd}$ 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 midpoint.
b. the student used incorrect coordinates when calculating the midpoint.
c. the student swapped the x - and y - values when calculating the midpoint.
d. the student did not add the x - and y - coordinates when calculating the midpoint.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-4,y_1 = 5,x_2=-1,y_2=-4$.

Step2: Analyze student's work

The student wrote $\frac{-4-(-1)}{2}$ and $\frac{5-(-4)}{2}$ instead of $\frac{-4+( - 1)}{2}$ and $\frac{5+( - 4)}{2}$. The student did not add the $x$ - and $y$ - coordinates as required by the mid - point formula.

Answer:

D. The student did not add the x - and y - coordinates when calculating the midpoint.