Perpendicular Lines (Copy)
Question 1
Find the gradient of a line perpendicular to y = 2x + 3.
Question 2
Find the gradient of a line perpendicular to y = –3x + 5.
Question 3
Find the equation of the line perpendicular to y = 4x – 1 passing through (0,2).
Question 4
Find the equation of the line perpendicular to y = –½x + 7 that passes through (–4,1).
Question 5
Find the equation of the line perpendicular to y = 5x + 2 and passing through (3,–1).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 6
Find the equation of the line perpendicular to y = –2x + 4 through (–2,6).
Question 7
Find the equation of the perpendicular bisector of the line joining A(0,0) and B(4,4).
Question 8
Find the equation of the perpendicular bisector of the line joining A(–6,2) and B(2,6).
Question 9
Find the equation of the line perpendicular to y = –¾x + 1 passing through (0,–2).
Question 10
Find the equation of the line perpendicular to y = 7x – 9 through (2,5).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 11
Find the equation of the perpendicular bisector of AB where A(–3,8) and B(9,–2).
Question 12
Find the gradient of a line perpendicular to y = –x + 4.
Question 13
Find the equation of the line perpendicular to y = 3x – 5 through (6,–7).
Question 14
Find the equation of the perpendicular bisector of AB where A(–4,–2), B(4,6).
Question 15
Find the equation of the line perpendicular to y = –2/3x + 1 through (3,0).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 16
Find the equation of the perpendicular bisector of PQ where P(–1,2) and Q(5,–4).
Question 17
Find the gradient of a line perpendicular to y = –7x + 1.
Question 18
Find the equation of the line perpendicular to y = ½x – 6 through (–2,3).
Question 19
Find the equation of the line perpendicular to y = –9x + 8 passing through (0,0).
Question 20
Find the equation of the perpendicular bisector of AB where A(–8,–4) and B(0,0).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 21
Find the equation of the line perpendicular to y = –5x – 2 through (2,–3).
Question 22
Find the gradient of a line perpendicular to y = ⅔x – 7.
Question 23
Find the equation of the perpendicular bisector of line joining A(–10,2), B(4,–6).
Question 24
Find the equation of the line perpendicular to y = –¼x + 3 through (8,0).
Question 25
Find the equation of the line perpendicular to y = 8x – 4 passing through (–2,–6).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 26
Find the equation of the line perpendicular to y = –1/5x + 3 through (0,7).
Question 27
Find the equation of the perpendicular bisector of PQ where P(–3,–3) and Q(5,5).
Question 28
Find the equation of the line perpendicular to y = –11x + 2 through (1,1).
Question 29
Find the equation of the line perpendicular to y = –2x + 9 through (–4,–1).
Question 30
Find the equation of the perpendicular bisector of line joining A(2,–6) and B(6,2).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
1.
y = 2x + 3 → m = 2.
Perpendicular slope = –1/2.
2.
y = –3x + 5 → m = –3.
Perpendicular slope = 1/3.
3.
y = 4x – 1 → m = 4 → perpendicular slope = –1/4.
Through (0,2): y – 2 = –¼(x – 0) → y = –¼x + 2.
4.
y = –½x + 7 → m = –½ → perpendicular slope = 2.
Through (–4,1): y – 1 = 2(x + 4) → y = 2x + 9.
5.
y = 5x + 2 → m = 5 → perpendicular slope = –1/5.
Through (3,–1): y + 1 = –1/5(x – 3) → y = –1/5x – 2/5.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
y = –2x + 4 → m = –2 → perpendicular slope = 1/2.
Through (–2,6): y – 6 = ½(x + 2) → y = ½x + 7.
7.
A(0,0), B(4,4): Midpoint = (2,2). Gradient AB = 1 → perpendicular slope = –1.
Equation: y – 2 = –1(x – 2) → y = –x + 4.
8.
A(–6,2), B(2,6): Midpoint = (–2,4). Gradient = (6–2)/(2–(–6)) = 4/8 = ½.
Perpendicular slope = –2.
Equation: y – 4 = –2(x + 2) → y = –2x.
9.
y = –¾x + 1 → slope = –¾ → perpendicular slope = 4/3.
Through (0,–2): y + 2 = 4/3(x – 0) → y = 4/3x – 2.
10.
y = 7x – 9 → slope = 7 → perpendicular slope = –1/7.
Through (2,5): y – 5 = –1/7(x – 2) → y = –1/7x + 37/7.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
A(–3,8), B(9,–2): Midpoint = (3,3). Gradient AB = (–2–8)/(9–(–3)) = –10/12 = –5/6.
Perpendicular slope = 6/5.
Equation: y – 3 = 6/5(x – 3) → y = 6/5x – 3/5.
12.
y = –x + 4 → slope = –1 → perpendicular slope = 1.
13.
y = 3x – 5 → slope = 3 → perpendicular slope = –1/3.
Through (6,–7): y + 7 = –1/3(x – 6) → y = –1/3x – 5.
14.
A(–4,–2), B(4,6): Midpoint = (0,2). Gradient AB = (6–(–2))/(4–(–4)) = 8/8 = 1.
Perpendicular slope = –1.
Equation: y – 2 = –1(x – 0) → y = –x + 2.
15.
y = –2/3x + 1 → slope = –2/3 → perpendicular slope = 3/2.
Through (3,0): y – 0 = 3/2(x – 3) → y = 3/2x – 9/2.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
16.
P(–1,2), Q(5,–4): Midpoint = (2,–1). Gradient PQ = (–4–2)/(5–(–1)) = –6/6 = –1.
Perpendicular slope = 1.
Equation: y + 1 = 1(x – 2) → y = x – 3.
17.
y = –7x + 1 → slope = –7 → perpendicular slope = 1/7.
18.
y = ½x – 6 → slope = ½ → perpendicular slope = –2.
Through (–2,3): y – 3 = –2(x + 2) → y = –2x – 1.
19.
y = –9x + 8 → slope = –9 → perpendicular slope = 1/9.
Through (0,0): y = 1/9x.
20.
A(–8,–4), B(0,0): Midpoint = (–4,–2). Gradient AB = (0–(–4))/(0–(–8)) = 4/8 = ½.
Perpendicular slope = –2.
Equation: y + 2 = –2(x + 4) → y = –2x – 10.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
21.
y = –5x – 2 → slope = –5 → perpendicular slope = 1/5.
Through (2,–3): y + 3 = 1/5(x – 2) → y = 1/5x – 17/5.
22.
y = ⅔x – 7 → slope = ⅔ → perpendicular slope = –3/2.
23.
A(–10,2), B(4,–6): Midpoint = (–3,–2). Gradient AB = (–6–2)/(4–(–10)) = –8/14 = –4/7.
Perpendicular slope = 7/4.
Equation: y + 2 = 7/4(x + 3) → y = 7/4x + 13/4.
24.
y = –¼x + 3 → slope = –¼ → perpendicular slope = 4.
Through (8,0): y – 0 = 4(x – 8) → y = 4x – 32.
25.
y = 8x – 4 → slope = 8 → perpendicular slope = –1/8.
Through (–2,–6): y + 6 = –1/8(x + 2) → y = –1/8x – 25/4.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
26.
y = –1/5x + 3 → slope = –1/5 → perpendicular slope = 5.
Through (0,7): y – 7 = 5(x – 0) → y = 5x + 7.
27.
P(–3,–3), Q(5,5): Midpoint = (1,1). Gradient PQ = (5–(–3))/(5–(–3)) = 8/8 = 1.
Perpendicular slope = –1.
Equation: y – 1 = –1(x – 1) → y = –x + 2.
28.
y = –11x + 2 → slope = –11 → perpendicular slope = 1/11.
Through (1,1): y – 1 = 1/11(x – 1) → y = 1/11x + 10/11.
29.
y = –2x + 9 → slope = –2 → perpendicular slope = ½.
Through (–4,–1): y + 1 = ½(x + 4) → y = ½x + 1.
30.
A(2,–6), B(6,2): Midpoint = (4,–2). Gradient AB = (2–(–6))/(6–2) = 8/4 = 2.
Perpendicular slope = –½.
Equation: y + 2 = –½(x – 4) → y = –½x.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course