Answer:
p = 11
Step-by-step explanation:
Let's start by finding the slope of line CD:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the given coordinates into the equation:
[tex]Slope=\frac{5-(-1)}{-4-3}=\frac{5+1}{-7}=-\frac{6}{7}[/tex]
Parallel lines have the same slope. This means we can plug the slope of line CD in to find p (in this case p is [tex]x_2[/tex])...
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]-\frac{6}{7}=\frac{-7-5}{p-(-3)}\\-\frac{6}{7}=\frac{-12}{p+3}[/tex]
Cross multiply (multiply numerator of first fraction by denominator of second and vice versa):
[tex]6(p+3)=(-7)(-12)[/tex]
Distribute:
[tex]6p+18=84[/tex]
Subtract 18 from both sides:
[tex]6p=66[/tex]
Divide both sides by 6
[tex]p=11[/tex]
