What is the slope of the line perpendicular to the line passing through the points (−4,5) and (3,−2)?
- A2
- B3/7
- C-3/7
- D1
Solution & Step-by-step Explanation
1. Find the slope (m
1
) of the line passing through (−4,5) and (3,−2):
m
1
=
x
2
−x
1
y
2
−y
1
=
3−(−4)
−2−5
=
7
−7
=−1
Find the slope (m
2
) of the perpendicular line:
The product of the slopes of two perpendicular lines is −1:
m
1
×m
2
=−1
−1×m
2
=−1
m
2
=1
Therefore, the slope of the perpendicular line is 1.
1
) of the line passing through (−4,5) and (3,−2):
m
1
=
x
2
−x
1
y
2
−y
1
=
3−(−4)
−2−5
=
7
−7
=−1
Find the slope (m
2
) of the perpendicular line:
The product of the slopes of two perpendicular lines is −1:
m
1
×m
2
=−1
−1×m
2
=−1
m
2
=1
Therefore, the slope of the perpendicular line is 1.