Answer:
The slope of line MN is two thirds,
The slope of line RS is negative three-halves
and line RS is perpendicular to both line MN and PQ
Step-by-step explanation:
For the first two, I found the slope using the slope formula, and I know the third one is correct because that is what it says in the very beginning.
Hope this helped, sorry if it is a little hard to understand, it was pretty hard to understand. :)
The following statements are true:
The formula for finding the slope of a line is expressed as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Get the slope of MN:
For the line MN with coordinates M(-3, -1) and (3, 3).
[tex]m=\frac{3-(-1)}{3-(-3)}\\m=\frac{3+1}{3+3}\\m=\frac{4}{6}\\m_{mn}=\frac{2}{3}[/tex]
Get the slope of PQ;
For the line PQ with coordinates M(-3, -4) and (3, 0.5)
[tex]m=\frac{0.5-(-4)}{3-(-3)}\\m=\frac{0.5+4}{3+3}\\m=\frac{4.5}{6}\\m_{pq}=\frac{45}{60}\\m_{pq}=\frac{3}{4}[/tex]
Get the slope of RS
For the line RS with coordinates M(-2, 4) and (2, -2)
[tex]m=\frac{-2-4}{2-(-2)}\\m=\frac{-6}{2+2}\\m=\frac{-6}{4}\\m_{rs}=\frac{-3}{2}[/tex]
For two lines to perpendicular, hence;
M = -1/m
From the derives slopes, we can see that;
[tex]m_{rs} = \frac{-1}{m_{mn}}\\m_{rs}= \frac{-1}{\frac{2}{3} }\\m_{rs}=\frac{-3}{2}[/tex]
This shows that the lines MN and RS are perpendicular.
Based on the above calculations, the following statements are true:
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