Question

point h lies on $overline{fg}$, where f is located at (-3.5, -11) and g is located at (4.5, -5). the ratio of fh to gh is 1:3. what is the sum of the coordinates of h? write your answer as an integer or decimal.

Explanation:

Step1: Find x - coordinate of H

Use the section - formula for x - coordinate $x=\frac{m_1x_2 + m_2x_1}{m_1 + m_2}$, where $m_1:m_2 = 1:3$, $x_1=-3.5$, $x_2 = 4.5$.
$x=\frac{1\times4.5+3\times(-3.5)}{1 + 3}=\frac{4.5-10.5}{4}=\frac{-6}{4}=-1.5$

Step2: Find y - coordinate of H

Use the section - formula for y - coordinate $y=\frac{m_1y_2 + m_2y_1}{m_1 + m_2}$, where $m_1:m_2 = 1:3$, $y_1=-11$, $y_2=-5$.
$y=\frac{1\times(-5)+3\times(-11)}{1 + 3}=\frac{-5-33}{4}=\frac{-38}{4}=-9.5$

Step3: Calculate the sum of coordinates

Sum of coordinates of H is $x + y=-1.5+( - 9.5)=-11$

Answer:

$-11$