Question

(04.03 lc)
grace has a segment with endpoints c(3, 4) and d(11, 3) that is divided by a point e such that ce and de form a 3:5 ratio. she knows the distance between the x coordinates is 8 units. which of the following fractions will let her find the x coordinate for point e?
options: (\frac{3}{5}), (\frac{5}{3}), (\frac{3}{8}), (\frac{5}{8})

Explanation:

Step1: Identify segment ratio total

Total parts = $3 + 5 = 8$

Step2: Fraction for CE portion

Fraction = $\frac{\text{CE parts}}{\text{Total parts}} = \frac{3}{8}$

Step3: Verify x-coordinate calculation logic

To find E's x-coordinate: $x_E = x_C + \frac{3}{8} \times (\text{total x-distance})$
This uses the fraction $\frac{3}{8}$ to scale the x-distance.

Answer:

$\boldsymbol{\frac{3}{8}}$ (Option: $\boldsymbol{\frac{3}{8}}$)