Answer:
Lines a and b are parallel
Lines a and c are perpendicular
Lines d and c are perpendicular
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
Part 1) Find the slope of Line a
we have the points
(-3,4) and (3,6)
substitute in the formula
simplify
Part 2) Find the slope of Line b
we have the points
(-10,-3) and (-8,3)
substitute in the formula
Part 3) Find the slope of Line c
we have the points
(0,5) and (3,-4)
substitute in the formula
Part 4) Find the slope of Line d
we have the points
(4,-7) and (13,-4)
substitute in the formula
simplify
Part 5) Compare the slopes
Remember that
If two lines are parallel then their slopes are the same
If two lines are perpendicular then their slopes are opposite reciprocal
we have
therefore
Lines a and b are parallel (slopes are equal)
Lines a and c are perpendicular (slopes are opposite reciprocal)
Lines d and c are perpendicular (slopes are opposite reciprocal)