Answer:
The sum of the slopes of line b and line c is 0
Step-by-step explanation:
Verify each statement
case a) The sum of the slopes of line b and line c is 0
we know that
Line b and line c are perpendicular lines
If two lines are perpendicular, then their slopes are opposite reciprocal
If the slope of line c is n
then the slope of line b is -1/n
[tex]-\frac{1}{n}+n=0[/tex]
Solve for n
[tex]n^{2}=1[/tex]
[tex]n=\pm1[/tex]
That means -----> This statement is true only when the slopes of the perpendicular lines are 1 and -1
therefore
NOT always true
case b) Line a and line b have the same slope
This statement is always true, because the lines are parallel
Remember that
If two lines are parallel, then the lines have the same slope
case c) The product of the slopes of line a and line c is -1
This statement is always true, because the lines are perpendicular
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
case d) The product of the slopes of line c and line b is -1
This statement is always true, because the lines are perpendicular
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
