Length and Midpoint (Copy)
Question 1
Find the length and midpoint of the line joining A(0,0) and B(3,4).
Question 2
Calculate the length and midpoint of the line segment from P(–2,5) to Q(4,–1).
Question 3
Find the distance between M(1,2) and N(7,8). Also find the midpoint.
Question 4
Calculate the length and midpoint of the line between X(–3,–4) and Y(5,2).
Question 5
Find the distance and midpoint of AB if A(0,5) and B(12,5).
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 6
Calculate the distance and midpoint of PQ where P(–6,0) and Q(–6,8).
Question 7
Find the length and midpoint of the line joining A(–2,–2) and B(6,–2).
Question 8
Calculate the distance and midpoint of MN where M(–5,–1) and N(2,3).
Question 9
Find the length and midpoint of the line joining A(4,7) and B(–2,–5).
Question 10
Find the distance and midpoint between P(–8,4) and Q(4,–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
Question 11
Calculate the length and midpoint of line between A(2,2) and B(2,–6).
Question 12
Find the distance and midpoint between X(0,–3) and Y(–4,–6).
Question 13
Find the distance between P(–3,–3) and Q(3,3). Also state the midpoint.
Question 14
Calculate the length and midpoint of the line between R(5,–2) and S(1,6).
Question 15
Find the distance and midpoint between A(–7,–4) and B(–1,–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
Question 16
Calculate length and midpoint of the line between C(0,0) and D(–12,9).
Question 17
Find distance and midpoint between A(–2,5) and B(10,–7).
Question 18
Find distance and midpoint of PQ if P(3,–4) and Q(–3,12).
Question 19
Calculate length and midpoint of line between X(–8,–6) and Y(–2,0).
Question 20
Find the distance and midpoint between A(–9,3) and B(9,–3).
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 length and midpoint of line joining A(7,1) and B(1,13).
Question 22
Calculate distance and midpoint of PQ where P(–4,–8) and Q(8,0).
Question 23
Find length and midpoint between X(2,–5) and Y(–10,–1).
Question 24
Find distance and midpoint of the line joining A(–3,0) and B(9,–12).
Question 25
Calculate the distance and midpoint of line segment between P(4,–9) and Q(–8,3).
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 length and midpoint of line between A(6,6) and B(–6,–6).
Question 27
Find the distance and midpoint of PQ where P(–5,9) and Q(7,–3).
Question 28
Find distance and midpoint between X(–7,–7) and Y(7,7).
Question 29
Find distance and midpoint of line joining A(–2,–9) and B(10,15).
Question 30
Find the length and midpoint of the line between M(–4,–2) and N(8,10).
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
1.
A(0,0), B(3,4)
Length = √((3–0)² + (4–0)²) = √(9+16) = √25 = 5
Midpoint = ((0+3)/2 , (0+4)/2) = (1.5 , 2)
2.
P(–2,5), Q(4,–1)
Length = √((4–(–2))² + (–1–5)²) = √(6² + (–6)²) = √(36+36) = √72 = 6√2
Midpoint = ((–2+4)/2 , (5+(–1))/2) = (1 , 2)
3.
M(1,2), N(7,8)
Length = √((7–1)² + (8–2)²) = √(36+36) = √72 = 6√2
Midpoint = ((1+7)/2 , (2+8)/2) = (4 , 5)
4.
X(–3,–4), Y(5,2)
Length = √((5–(–3))² + (2–(–4))²) = √(8²+6²) = √(64+36) = √100 = 10
Midpoint = ((–3+5)/2 , (–4+2)/2) = (1 , –1)
5.
A(0,5), B(12,5)
Length = √((12–0)² + (5–5)²) = √(144+0) = 12
Midpoint = ((0+12)/2 , (5+5)/2) = (6 , 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.
P(–6,0), Q(–6,8)
Length = √((–6–(–6))²+(8–0)²) = √(0+64) = 8
Midpoint = ((–6–6)/2 , (0+8)/2) = (–6 , 4)
7.
A(–2,–2), B(6,–2)
Length = √((6–(–2))²+(–2–(–2))²) = √(8²+0) = 8
Midpoint = ((–2+6)/2 , (–2–2)/2) = (2 , –2)
8.
M(–5,–1), N(2,3)
Length = √((2–(–5))²+(3–(–1))²) = √(7²+4²) = √(49+16) = √65
Midpoint = ((–5+2)/2 , (–1+3)/2) = (–1.5 , 1)
9.
A(4,7), B(–2,–5)
Length = √((–2–4)²+(–5–7)²) = √((–6)²+(–12)²) = √(36+144) = √180 = 6√5
Midpoint = ((4–2)/2 , (7–5)/2) = (1 , 1)
10.
P(–8,4), Q(4,–2)
Length = √((4–(–8))²+(–2–4)²) = √(12²+(–6)²) = √(144+36) = √180 = 6√5
Midpoint = ((–8+4)/2 , (4–2)/2) = (–2 , 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
11.
A(2,2), B(2,–6)
Length = √((2–2)²+(–6–2)²) = √(0+(–8)²) = √64 = 8
Midpoint = ((2+2)/2 , (2–6)/2) = (2 , –2)
12.
X(0,–3), Y(–4,–6)
Length = √((–4–0)²+(–6–(–3))²) = √((–4)²+(–3)²) = √(16+9) = √25 = 5
Midpoint = ((0–4)/2 , (–3–6)/2) = (–2 , –4.5)
13.
P(–3,–3), Q(3,3)
Length = √((3–(–3))²+(3–(–3))²) = √(6²+6²) = √72 = 6√2
Midpoint = ((–3+3)/2 , (–3+3)/2) = (0 , 0)
14.
R(5,–2), S(1,6)
Length = √((1–5)²+(6–(–2))²) = √((–4)²+(8)²) = √(16+64) = √80 = 4√5
Midpoint = ((5+1)/2 , (–2+6)/2) = (3 , 2)
15.
A(–7,–4), B(–1,–10)
Length = √((–1–(–7))²+(–10–(–4))²) = √(6²+(–6)²) = √72 = 6√2
Midpoint = ((–7–1)/2 , (–4–10)/2) = (–4 , –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
16.
C(0,0), D(–12,9)
Length = √((–12–0)²+(9–0)²) = √(144+81) = √225 = 15
Midpoint = ((0–12)/2 , (0+9)/2) = (–6 , 4.5)
17.
A(–2,5), B(10,–7)
Length = √((10–(–2))²+(–7–5)²) = √(12²+(–12)²) = √288 = 12√2
Midpoint = ((–2+10)/2 , (5–7)/2) = (4 , –1)
18.
P(3,–4), Q(–3,12)
Length = √((–3–3)²+(12–(–4))²) = √((–6)²+(16)²) = √(36+256) = √292
Midpoint = ((3–3)/2 , (–4+12)/2) = (0 , 4)
19.
X(–8,–6), Y(–2,0)
Length = √((–2–(–8))²+(0–(–6))²) = √(6²+6²) = √72 = 6√2
Midpoint = ((–8–2)/2 , (–6+0)/2) = (–5 , –3)
20.
A(–9,3), B(9,–3)
Length = √((9–(–9))²+(–3–3)²) = √(18²+(–6)²) = √(324+36) = √360 = 6√10
Midpoint = ((–9+9)/2 , (3–3)/2) = (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
21.
A(7,1), B(1,13)
Length = √((1–7)²+(13–1)²) = √((–6)²+12²) = √(36+144) = √180 = 6√5
Midpoint = ((7+1)/2 , (1+13)/2) = (4 , 7)
22.
P(–4,–8), Q(8,0)
Length = √((8–(–4))²+(0–(–8))²) = √(12²+8²) = √(144+64) = √208 = 4√13
Midpoint = ((–4+8)/2 , (–8+0)/2) = (2 , –4)
23.
X(2,–5), Y(–10,–1)
Length = √((–10–2)²+(–1–(–5))²) = √((–12)²+4²) = √(144+16) = √160 = 4√10
Midpoint = ((2–10)/2 , (–5–1)/2) = (–4 , –3)
24.
A(–3,0), B(9,–12)
Length = √((9–(–3))²+(–12–0)²) = √(12²+(–12)²) = √(144+144) = √288 = 12√2
Midpoint = ((–3+9)/2 , (0–12)/2) = (3 , –6)
25.
P(4,–9), Q(–8,3)
Length = √((–8–4)²+(3–(–9))²) = √((–12)²+12²) = √(144+144) = √288 = 12√2
Midpoint = ((4–8)/2 , (–9+3)/2) = (–2 , –3)
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.
A(6,6), B(–6,–6)
Length = √((–6–6)²+(–6–6)²) = √((–12)²+(–12)²) = √(144+144) = √288 = 12√2
Midpoint = ((6–6)/2 , (6–6)/2) = (0 , 0)
27.
P(–5,9), Q(7,–3)
Length = √((7–(–5))²+(–3–9)²) = √(12²+(–12)²) = √288 = 12√2
Midpoint = ((–5+7)/2 , (9–3)/2) = (1 , 3)
28.
X(–7,–7), Y(7,7)
Length = √((7–(–7))²+(7–(–7))²) = √(14²+14²) = √(196+196) = √392 = 14√2
Midpoint = ((–7+7)/2 , (–7+7)/2) = (0 , 0)
29.
A(–2,–9), B(10,15)
Length = √((10–(–2))²+(15–(–9))²) = √(12²+24²) = √(144+576) = √720 = 12√5
Midpoint = ((–2+10)/2 , (–9+15)/2) = (4 , 3)
30.
M(–4,–2), N(8,10)
Length = √((8–(–4))²+(10–(–2))²) = √(12²+12²) = √288 = 12√2
Midpoint = ((–4+8)/2 , (–2+10)/2) = (2 , 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