Question

surveyors typically use a unit of measure called a rod, which equals 16 feet. a surveyor was called upon to find the location of a new interpretive center at a park and the park entrance. the surveyor plotted the points shown on a coordinate grid of the park in units of 1 rod. the line between the interpretive center and park headquarters is perpendicular to the line connecting the park headquarters and park entrance. using the coordinates, determine the slope of the line between the park headquarters and interpretive center. use rise / run for the park headquarters to entrance count up 25 / over 10 slope = ? now for headquarters to interpretive what slope would be perpendicular? park entrance (25,25) interpretive center park headquarters (15,0) n s w e

Explanation:

Step1: Calculate slope of park headquarters - entrance line

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the line from Park Headquarters $(15,0)$ to Park Entrance $(25,25)$, we have $m_1=\frac{25 - 0}{25 - 15}=\frac{25}{10}=\frac{5}{2}$.

Step2: Find slope of perpendicular line

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the line from Park Headquarters to Interpretive Center be $m_2$. Then $m_1\times m_2=-1$. Since $m_1 = \frac{5}{2}$, we can solve for $m_2$: $m_2=-\frac{2}{5}$.

Answer:

$-\frac{2}{5}$