Question

which of the following fractions compares bc to bd?

\\(\frac{2}{3}\\)
\\(\frac{5}{2}\\)
\\(\frac{2}{5}\\)
\\(\frac{3}{2}\\)

Explanation:

Determine the lengths of segments BC and BD

The points lie on a vertical line where \(x = 1\).
The y-coordinates of the points are:

• \(B\) is at \(y = 0\)
• \(C\) is at \(y = 2\)
• \(D\) is at \(y = 3\)

Calculate the lengths:

• \(BC = |2 - 0| = 2\)
• \(BD = |3 - 0| = 3\)

Compare BC to BD as a fraction

The ratio comparing \(BC\) to \(BD\) is:

$$ \frac{BC}{BD} = \frac{2}{3} $$

Match with the given options

The options shown in the image are:

• First option: \(\frac{2}{3}\)
• Second option: \(\frac{5}{2}\)
• Third option: \(\frac{2}{5}\)
• Fourth option: \(\frac{3}{2}\)

The correct option is \(\frac{2}{3}\).

Answer:

• (A) \(\frac{2}{3}\) (Correct answer)
• (B) \(\frac{5}{2}\)
• (C) \(\frac{2}{5}\)
• (D) \(\frac{3}{2}\)