Question content area top

Question

Part 1
Describe and correct the error a student made in finding the midpoint of CD overbar with ​C(minus​4,5) and ​D(minus​1,minus​4).
Question content area bottom
Part 1
Choose the correct answer below.
A.
The student swapped the​ x- and​ y-values when calculating the midpoint.
B.
The student used incorrect coordinates when calculating the midpoint.
C.
The student did not add the​ x- and​ y-coordinates when calculating the midpoint.
Your answer is correct.D.
The student did not divide the numerator and denominator by 2 when calculating the midpoint.
Part 2
The correct answer is
  
enter your response here.
​(Type an ordered​ pair, using integers or​ fractions.)

Answer 1

To find the midpoint of a line segment defined by the endpoints \( C(-4, 5) \) and \( D(-1, -4) \), we use the midpoint formula:

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

In this case, the coordinates of point \( C \) are \( (x_1, y_1) = (-4, 5) \) and the coordinates of point \( D \) are \( (x_2, y_2) = (-1, -4) \).

Now, let's calculate the midpoint step by step:

1. Calculate the average of the x-coordinates:

\[ \frac{-4 + (-1)}{2} = \frac{-4 - 1}{2} = \frac{-5}{2} \]

2. Calculate the average of the y-coordinates:

\[ \frac{5 + (-4)}{2} = \frac{5 - 4}{2} = \frac{1}{2} \]

So, the midpoint \( M \) is:

\[ M = \left( \frac{-5}{2}, \frac{1}{2} \right) \]

Part 1 Error Description

The correct answer to the description of the student's error is:

D. The student did not divide the numerator and denominator by 2 when calculating the midpoint.

Part 2 Correct Answer

The correct midpoint is:

\[ \left( -\frac{5}{2}, \frac{1}{2} \right) \]

In ordered pair format, you can state:

\(-\frac{5}{2}, \frac{1}{2}\) as your final answer.