Question

Find the equation of the line passing through (−3,5) and perpendicular to the line through the points (2,5)(−3,6).

• A. (A) x+y+20=0
• B. (B) x−y+20=0
• C. (C) x+5y+20=0
• D. (D) 5x−y+20=0

Answer 1

Answer: (D)

(D) 5x−y+20=0

Answer 2

Explanation:
The equation of the line passing through (x1,y1) with the slope m is:(y−y1)=m(x−x1)The slope of line passing through the points (x1,y1) and (x2,y2) is:=y2−y1x2−x1The slope of line passing through the points (2,5)(−3,6) is =6−5−3−2⇒m1=1−5=−15The two non-vertical lines are perpendicular to each other only if and only if their slopes are negative reciprocals of each other.The slope of perpendicular to the line through the points (2,5)(−3,6) is m2=−1 m1⇒m2=5The equation of the line passing through (x1,y1)=(−3,5) and perpendicular to the line through the points (2,5)(−3,6) is:(y−y1)=m(x−x1)⇒(y−5)=5(x+3)⇒5x−y+20=0Hence, the correct option is (D).