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 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.
D.
The student did not divide the numerator and denominator by 2 when calculating the midpoint.
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.
D.
The student did not divide the numerator and denominator by 2 when calculating the midpoint.
Answers
GPT-4o mini
To find the midpoint of a line segment defined by points \( C(-4, 5) \) and \( D(-1, -4) \), we use the midpoint formula:
\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Given:
- \( C(x_1, y_1) = (-4, 5) \)
- \( D(x_2, y_2) = (-1, -4) \)
Let's plug in the values into the formula:
1. For the \( x \)-coordinate:
\[
\frac{-4 + (-1)}{2} = \frac{-4 - 1}{2} = \frac{-5}{2} = -2.5
\]
2. For the \( y \)-coordinate:
\[
\frac{5 + (-4)}{2} = \frac{5 - 4}{2} = \frac{1}{2} = 0.5
\]
So the correct midpoint is:
\[
\left(-2.5, 0.5\right)
\]
Now, to identify the error made by the student:
- A. **The student swapped the x- and y-values when calculating the midpoint.** (This would mean they mixed up which coordinates were x's and which were y's.)
- B. **The student used incorrect coordinates when calculating the midpoint.** (This would mean they used values other than those given for points C and D.)
- C. **The student did not add the x- and y-coordinates when calculating the midpoint.** (This would indicate they didn't perform the addition for the coordinates correctly.)
- D. **The student did not divide the numerator and denominator by 2 when calculating the midpoint.** (This implies that they skipped the division step.)
Based on the problem, the most likely error is **A** if the student accidentally swapped the x and y values. However, if the student did get a wrong result without providing any intermediate steps or specific incorrect entries, option **B** might also fit.
Without seeing the student's work, it's challenging to pinpoint the exact mistake, but option **A** seems plausible if the resulting coordinates reflect a mix-up of positions.
If you know the particular incorrect calculation the student provided, you could more accurately choose between A, B, C, or D. However, from a general standpoint, **A** is the most likely error in such cases. If you verify the values the student obtained, you could ensure no other option applies better.
\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Given:
- \( C(x_1, y_1) = (-4, 5) \)
- \( D(x_2, y_2) = (-1, -4) \)
Let's plug in the values into the formula:
1. For the \( x \)-coordinate:
\[
\frac{-4 + (-1)}{2} = \frac{-4 - 1}{2} = \frac{-5}{2} = -2.5
\]
2. For the \( y \)-coordinate:
\[
\frac{5 + (-4)}{2} = \frac{5 - 4}{2} = \frac{1}{2} = 0.5
\]
So the correct midpoint is:
\[
\left(-2.5, 0.5\right)
\]
Now, to identify the error made by the student:
- A. **The student swapped the x- and y-values when calculating the midpoint.** (This would mean they mixed up which coordinates were x's and which were y's.)
- B. **The student used incorrect coordinates when calculating the midpoint.** (This would mean they used values other than those given for points C and D.)
- C. **The student did not add the x- and y-coordinates when calculating the midpoint.** (This would indicate they didn't perform the addition for the coordinates correctly.)
- D. **The student did not divide the numerator and denominator by 2 when calculating the midpoint.** (This implies that they skipped the division step.)
Based on the problem, the most likely error is **A** if the student accidentally swapped the x and y values. However, if the student did get a wrong result without providing any intermediate steps or specific incorrect entries, option **B** might also fit.
Without seeing the student's work, it's challenging to pinpoint the exact mistake, but option **A** seems plausible if the resulting coordinates reflect a mix-up of positions.
If you know the particular incorrect calculation the student provided, you could more accurately choose between A, B, C, or D. However, from a general standpoint, **A** is the most likely error in such cases. If you verify the values the student obtained, you could ensure no other option applies better.