Question

the coordinates of the endpoints of (overline{tu}) are (t(2,4)) and (u(11,13)). point (v) is on (overline{tu}) and divides it such that (tv:uv) is (7:2). what are the coordinates of (v)? write your answers as integers or decimals.

Explanation:

Step1: Find x - coordinate of V

Use the section - formula for x - coordinate $x=\frac{m_1x_2 + m_2x_1}{m_1 + m_2}$, where $(x_1,y_1)=(2,4)$ is the coordinate of $T$, $(x_2,y_2)=(11,13)$ is the coordinate of $U$, $m_1 = 7$ and $m_2=2$.
$x=\frac{7\times11+2\times2}{7 + 2}=\frac{77 + 4}{9}=\frac{81}{9}=9$

Step2: Find y - coordinate of V

Use the section - formula for y - coordinate $y=\frac{m_1y_2 + m_2y_1}{m_1 + m_2}$.
$y=\frac{7\times13+2\times4}{7 + 2}=\frac{91+8}{9}=\frac{99}{9}=11$

Answer:

$(9,11)$