Question

describe and correct the error a student made in finding the mid - point of $overline{cd}$ with $c(-4,5)$ and $d(-1,-4)$. choose the correct answer below. a. the student used incorrect coordinates when calculating the mid - point. b. the student did not add the x - and y - coordinates when calculating the mid - point. c. the student did not divide the numerator and denominator by 2 when calculating the mid - point. d. the student swapped the x - and y - values 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 $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-4,y_1 = 5,x_2=-1,y_2=-4$.

Step2: Analyze error

The error is that the student did not add the $x$ - and $y$ - coordinates when calculating the mid - point.

Step3: Calculate mid - point

$x$ - coordinate of mid - point: $\frac{-4+( - 1)}{2}=\frac{-4 - 1}{2}=-\frac{5}{2}$
$y$ - coordinate of mid - point: $\frac{5+( - 4)}{2}=\frac{5 - 4}{2}=\frac{1}{2}$

Answer:

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