Question
Which of the following fractions compares BC to BD?
coordinate plane with segment BD at B 0 comma 1 and D 3 comma 1; point C is on segment BD and 2 comma 1
two thirds
five halves
two fifths
three halves
Answers
GPT-4o mini
To compare the lengths of segments \( BC \) and \( BD \), we first need to determine the lengths of these segments based on their coordinates.
1. **Coordinates of points:**
- \( B (0, 1) \)
- \( D (3, 1) \)
- \( C (2, 1) \)
2. **Length of segment \( BD \):**
The length of segment \( BD \) can be calculated as follows:
\[
BD = |x_D - x_B| = |3 - 0| = 3
\]
3. **Length of segment \( BC \):**
The length of segment \( BC \) can be calculated similarly:
\[
BC = |x_C - x_B| = |2 - 0| = 2
\]
4. **Setting up the fraction to compare \( BC \) to \( BD \):**
To find the fraction that compares \( BC \) to \( BD \), we set up the fraction:
\[
\frac{BC}{BD} = \frac{2}{3}
\]
Thus, the fraction that compares \( BC \) to \( BD \) is \( \frac{2}{3} \).
The correct answer is **two thirds**.
1. **Coordinates of points:**
- \( B (0, 1) \)
- \( D (3, 1) \)
- \( C (2, 1) \)
2. **Length of segment \( BD \):**
The length of segment \( BD \) can be calculated as follows:
\[
BD = |x_D - x_B| = |3 - 0| = 3
\]
3. **Length of segment \( BC \):**
The length of segment \( BC \) can be calculated similarly:
\[
BC = |x_C - x_B| = |2 - 0| = 2
\]
4. **Setting up the fraction to compare \( BC \) to \( BD \):**
To find the fraction that compares \( BC \) to \( BD \), we set up the fraction:
\[
\frac{BC}{BD} = \frac{2}{3}
\]
Thus, the fraction that compares \( BC \) to \( BD \) is \( \frac{2}{3} \).
The correct answer is **two thirds**.