To find the slope of line \( s \) which is perpendicular to line \( r \), we first need to determine the slope of line \( r \).
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
For points \( (10, 9) \) and \( (3, 14) \):
- \( (x_1, y_1) = (10, 9) \)
- \( (x_2, y_2) = (3, 14) \)
Substituting these values into the slope formula:
\[ m_r = \frac{14 - 9}{3 - 10} = \frac{5}{-7} = -\frac{5}{7} \]
Now we know that the slope of line \( r \) is \( -\frac{5}{7} \).
The slope of a line \( s \) that is perpendicular to line \( r \) is the negative reciprocal of the slope of line \( r \). The negative reciprocal of \( m_r \) is calculated as follows:
-
Take the reciprocal: \[ \text{Reciprocal of } -\frac{5}{7} = -\frac{7}{5} \]
-
Change the sign (to get the negative reciprocal): \[ \text{Negative reciprocal} = \frac{7}{5} \]
Therefore, the slope of line \( s \) is:
\[ \boxed{\frac{7}{5}} \]
1 answer