# Thread: Slopes Help

1. ## Slopes Help

Slopes

1.) Using slopes, determine which of the set of three points lie on a straight line:
$\displaystyle (-1,-2),(6,-5),(-10,2)$

2.) The line segment drawn from $\displaystyle P(x,3)$ to $\displaystyle (4,1)$ is perpendicular to the segment drawn from $\displaystyle (-5,-6)$ to $\displaystyle (4,1)$. Find the value of x.

Thanks a bunch

2. Originally Posted by ^_^Engineer_Adam^_^
2.) The line segment drawn from $\displaystyle P(x,3)$ to $\displaystyle (4,1)$ is perpendicular to the segment drawn from $\displaystyle (-5,-6)$ to $\displaystyle (4,1)$. Find the value of x.
To find the slope of a line use the equation:
$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$

Slopes that are perpendicular are negative inverses:
$\displaystyle m_2 = -\frac{1}{m_1}$

-Dan

3. Originally Posted by ^_^Engineer_Adam^_^
Slopes

1.) Using slopes, determine which of the set of three points lie on a straight line:
$\displaystyle (-1,-2),(6,-5),(-10,2)$

2.) The line segment drawn from $\displaystyle P(x,3)$ to $\displaystyle (4,1)$ is perpendicular to the segment drawn from $\displaystyle (-5,-6)$ to $\displaystyle (4,1)$. Find the value of x.

Thanks a bunch
Hello,

to 1.) You have three points: A(-1, -2), B(6, -5), C(-10, 2).

If the slope between A and B is the same as the slope between B and C, then the three points lie on a straight line:
s means slope:

$\displaystyle s_{AB}=\frac{-2-(-5)}{-1-6}=\frac{3}{-7}$

$\displaystyle s_{BC}=\frac{2-(-5)}{-10-6}=\frac{7}{-16}$

Both slopes are not equal therefore the three points don't lie on a straight line.

to 2.) You have 3 points: P(x, 3), Q(4, 1) and B(-5, -6)

a) Calculate the slope between Q and B:
$\displaystyle s_{QB}=\frac{1-(-6)}{4-(-5)}=\frac{7}{9}$. Thus the perpendicular direction is: -9/7 (have a look at topsquark's post!)

The slope between P and Q should be equal to this perpendicular slope:

$\displaystyle s_{PQ}=\frac{3-1}{x-4}=-\frac{9}{7}$. Solve for x.

(I've got x = 22/9)

EB