Question

1. points d and n are on a number line. the expression \\(\frac{4}{7}\\)(point d) + \\(\frac{3}{7}\\)(point n) represents the point that partitions points d and n. what ratio are the points partitioned by?\

\\(\bigcirc\\) 3: 4\
\\(\bigcirc\\) 1: 2\
\\(\bigcirc\\) 2: 1\
\\(\bigcirc\\) 3: 2\
\\(\bigcirc\\) 2: 3\
\\(\bigcirc\\) 1: 5

Explanation:

Step1: Recall the section formula

The section formula for a point that divides the line segment joining two points \( D \) (with coordinate \( x_D \)) and \( N \) (with coordinate \( x_N \)) in the ratio \( m:n \) is given by \( \frac{n x_D + m x_N}{m + n} \).

Step2: Compare with the given expression

The given expression is \( \frac{4}{7}(x_D)+\frac{3}{7}(x_N) \), which can be written as \( \frac{3 x_N + 4 x_D}{4 + 3} \). Comparing with the section formula \( \frac{n x_D + m x_N}{m + n} \), we have \( n = 4 \) and \( m = 3 \). So the ratio \( m:n \) (the ratio of the segments from \( D \) to the partition point and from the partition point to \( N \)) is \( 3:4 \).

Answer:

3: 4