Question
Describe and correct the error a student made in finding the midpoint of CD overbar with C(minus4,5) and D(minus1,minus4).
Question content area bottom
Part 1
Choose the correct answer below.
A.
The student used incorrect coordinates when calculating the midpoint.
B.
The student swapped the x- and y-values when calculating the midpoint.
C.
The student did not add the x- and y-coordinates when calculating the midpoint.
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.)
Question content area bottom
Part 1
Choose the correct answer below.
A.
The student used incorrect coordinates when calculating the midpoint.
B.
The student swapped the x- and y-values when calculating the midpoint.
C.
The student did not add the x- and y-coordinates when calculating the midpoint.
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.)
Answers
GPT-4o mini
To find the midpoint \( M \) of the line segment \( CD \) with endpoints \( C(-4, 5) \) and \( D(-1, -4) \), we use the midpoint formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Substituting the coordinates of points \( C \) and \( D \):
- \( x_1 = -4 \), \( y_1 = 5 \)
- \( x_2 = -1 \), \( y_2 = -4 \)
Now substituting these values into the formula:
\[
M = \left( \frac{-4 + (-1)}{2}, \frac{5 + (-4)}{2} \right)
\]
This simplifies to:
\[
M = \left( \frac{-5}{2}, \frac{1}{2} \right)
\]
So the midpoint is:
\[
M = \left( -\frac{5}{2}, \frac{1}{2} \right)
\]
### Part 1
Correcting the student's error:
Examining the errors, the choices provided are:
A. The student used incorrect coordinates when calculating the midpoint.
B. The student swapped the x- and y-values when calculating the midpoint.
C. The student did not add the x- and y-coordinates when calculating the midpoint.
D. The student did not divide the numerator and denominator by 2 when calculating the midpoint.
To determine which option is accurate, we need to analyze possible mistakes:
1. An incorrect calculation of the coordinates would fall under A.
2. If they swapped x and y while using the formula, that would fit option B.
3. Option C would indicate they didn't perform the addition correctly.
4. Option D would indicate they incorrectly did not divide by 2.
Without more context about what the student actually did, it is difficult to select the precise wrong step, but typically the midpoint formula follows a routine process, which could lead to options A or D being more likely.
### Part 2
The correct answer, as derived above, is:
\[
M = \left( -\frac{5}{2}, \frac{1}{2} \right)
\]
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Substituting the coordinates of points \( C \) and \( D \):
- \( x_1 = -4 \), \( y_1 = 5 \)
- \( x_2 = -1 \), \( y_2 = -4 \)
Now substituting these values into the formula:
\[
M = \left( \frac{-4 + (-1)}{2}, \frac{5 + (-4)}{2} \right)
\]
This simplifies to:
\[
M = \left( \frac{-5}{2}, \frac{1}{2} \right)
\]
So the midpoint is:
\[
M = \left( -\frac{5}{2}, \frac{1}{2} \right)
\]
### Part 1
Correcting the student's error:
Examining the errors, the choices provided are:
A. The student used incorrect coordinates when calculating the midpoint.
B. The student swapped the x- and y-values when calculating the midpoint.
C. The student did not add the x- and y-coordinates when calculating the midpoint.
D. The student did not divide the numerator and denominator by 2 when calculating the midpoint.
To determine which option is accurate, we need to analyze possible mistakes:
1. An incorrect calculation of the coordinates would fall under A.
2. If they swapped x and y while using the formula, that would fit option B.
3. Option C would indicate they didn't perform the addition correctly.
4. Option D would indicate they incorrectly did not divide by 2.
Without more context about what the student actually did, it is difficult to select the precise wrong step, but typically the midpoint formula follows a routine process, which could lead to options A or D being more likely.
### Part 2
The correct answer, as derived above, is:
\[
M = \left( -\frac{5}{2}, \frac{1}{2} \right)
\]