Answer:
The lines are parallel i.e. KM || ST
Step-by-step explanation:
Given
K(-5,1) , M(-2,-8), and S(12,14), T(20,-10)
In order to find if the lines are parallel, perpendicular or neither slope will be used.
The slope of any line which passes from two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the formula
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
If two lines are parallel their slope is equal. If two lines are perpendicular the product of their slope is equal to -1
So, first slopes of both lines will be calculated.
Let m1 be the slope of KM
and
m2 be the slope of ST
In case of KM:
[tex](x_1,y_1) = (-5,1)\\(x_2,y_2) = (-2,-8)[/tex]
Putting the values in the formula for slope
[tex]m_1 = \frac{-8-1}{-2-(-5)}\\m_1 = \frac{-9}{-2+5}\\= \frac{-9}{3}\\= -3[/tex]
In case of ST:
[tex](x_1,y_1) = (12,14)\\(x_2,y_2) = (20,-10)[/tex]
Putting the values in the formula for slope
[tex]m_2 = \frac{-10-14}{20-12}\\= \frac{-24}{8}\\= -3[/tex]
As we can see that slope of both lines KM and ST are equal
i.e. m1 = m2 = -3
Hence,
The lines are parallel i.e. KM || ST
