Question

point t lies on \\(\overline{rs}\\) such that \\(rt:st\\) is \\(2:5\\). graph t.

Explanation:

Step1: Find coordinates of R and S

From the graph, \( R(-6, 5) \), \( S(8, -2) \).

Step2: Use section formula

For a point \( T(x, y) \) dividing \( \overline{RS} \) in ratio \( m:n = 2:5 \),
\( x=\frac{m x_S + n x_R}{m + n}=\frac{2\times8 + 5\times(-6)}{2 + 5}=\frac{16 - 30}{7}=\frac{-14}{7}=-2 \)
\( y=\frac{m y_S + n y_R}{m + n}=\frac{2\times(-2)+5\times5}{2 + 5}=\frac{-4 + 25}{7}=\frac{21}{7}=3 \)

Answer:

Point \( T \) has coordinates \( (-2, 3) \).