Answer:
The line m and line n are not parallel to each other.
line m ⊥ line k.
Step-by-step explanation:
See the diagram attached to this question.
The points (0,-4) and (-4,3) through which line m passes.
Therefore, the slope of line m is [tex]\frac{-4-3}{0-(-4)} =-\frac{7}{4}[/tex]
Now, line n passes through the points (1,2) and (3,-2).
Therefore, the slope of the line n is [tex]\frac{2-(-2)}{1-3}=-2[/tex]
Hence, the line m and line n are not parallel as their slopes are not equal. (Answer)
Again, the points (4,1) and (-3,-3) through which line k passes.
Therefore, the slope of the line k is [tex]\frac{1-(-3)}{4-(-3)} =\frac{4}{7}[/tex]
Hence, the product of slopes of line m and line k is [tex](-\frac{7}{4}) \times (\frac{4}{7} ) =-1[/tex].
So, line m ⊥ line k. (Answer)
{Since -1 will be the result if we multiply the slopes of two mutually perpendicular straight lines }
Answer:
1) No, the slopes are not equal
2) Yes, the slopes are negative reciprocals
Step-by-step explanation: