Question

find the coordinates of the point that partitions \\(overline{ab}\\) in the ratio 3:7. the point that partitions \\(overline{ab}\\) in the ratio 3:7 is \\(square\\). (simplify your answer. type an ordered pair.)

Explanation:

Step1: Identify coordinates of A and B

From the graph, \( A(-8, 4) \), \( B(12, -6) \), ratio \( m:n = 3:7 \).

Step2: Use section formula

The section formula for a point \((x,y)\) dividing \(\overline{AB}\) in ratio \( m:n \) is:
\( x = \frac{mx_2 + nx_1}{m + n} \), \( y = \frac{my_2 + ny_1}{m + n} \)

Substitute \( m = 3 \), \( n = 7 \), \( x_1 = -8 \), \( y_1 = 4 \), \( x_2 = 12 \), \( y_2 = -6 \):

For \( x \):
\( x = \frac{3(12) + 7(-8)}{3 + 7} = \frac{36 - 56}{10} = \frac{-20}{10} = -2 \)

For \( y \):
\( y = \frac{3(-6) + 7(4)}{3 + 7} = \frac{-18 + 28}{10} = \frac{10}{10} = 1 \)

Answer:

\((-2, 1)\)