Worksheet: Solving Equations to Find the Length of a Line Segment

In this worksheet, we will practice finding the length of a line segment by constructing a multistep linear equation and solving it.

Q1:

Find the length of 𝑋 𝑌 .

Q2:

𝐴 is the midpoint of 𝐵 𝐶 , where 𝐵 𝐴 = 1 0 𝑥 1 7 and 𝐴 𝐶 = 6 𝑥 + 7 . Find 𝑥 and 𝐵 𝐶 .

  • A 𝑥 = 2 . 5 , 𝐵 𝐶 = 4 4
  • B 𝑥 = 6 , 𝐵 𝐶 = 4 3
  • C 𝑥 = 1 . 5 , 𝐵 𝐶 = 3 2
  • D 𝑥 = 6 , 𝐵 𝐶 = 8 6
  • E 𝑥 = 2 . 5 , 𝐵 𝐶 = 1 6

Q3:

Find the value of 𝑥 given 𝑂 𝐴 = 𝑂 𝐵 .

Q4:

Point 𝑄 is on the line between 𝑃 and 𝑅 . If 𝑃 𝑄 = 2 𝑥 3 , 𝑄 𝑅 = 4 𝑥 + 8 , and 𝑃 𝑅 = 1 0 𝑥 5 , what is the length of 𝑃 𝑄 ?

Q5:

If 𝐶 divides 𝐴 𝐵 by the ratio 4 2 7 externally, find 𝐴 𝐶 𝐴 𝐵 and 𝐴 𝐵 𝐵 𝐶 .

  • A 𝐴 𝐶 𝐴 𝐵 = 2 3 2 7 , 𝐴 𝐵 𝐵 𝐶 = 4 2 3
  • B 𝐴 𝐶 𝐴 𝐵 = 2 3 4 , 𝐴 𝐵 𝐵 𝐶 = 2 7 2 3
  • C 𝐴 𝐶 𝐴 𝐵 = 2 7 2 3 , 𝐴 𝐵 𝐵 𝐶 = 2 3 4
  • D 𝐴 𝐶 𝐴 𝐵 = 4 2 3 , 𝐴 𝐵 𝐵 𝐶 = 2 3 2 7

Q6:

If 𝐶 divides 𝐵 𝐴 by a ratio of 1 1 2 5 internally, find 𝐴 𝐶 𝐵 𝐶 and 𝐴 𝐶 𝐴 𝐵 .

  • A 𝐴 𝐶 𝐵 𝐶 = 2 5 3 6 , 𝐴 𝐶 𝐴 𝐵 = 2 5 1 1
  • B 𝐴 𝐶 𝐵 𝐶 = 1 1 2 5 , 𝐴 𝐶 𝐴 𝐵 = 3 6 2 5
  • C 𝐴 𝐶 𝐵 𝐶 = 3 6 2 5 , 𝐴 𝐶 𝐴 𝐵 = 1 1 2 5
  • D 𝐴 𝐶 𝐵 𝐶 = 2 5 1 1 , 𝐴 𝐶 𝐴 𝐵 = 2 5 3 6

Q7:

Given that the points are evenly spaced along the line, find the length of 𝐹 𝐺 .

Q8:

Given that the points are evenly spaced along the line, find the length of 𝑅 𝑆 .

Q9:

In the following figure, points 𝐴 , 𝐵 , 𝐶 , 𝐷 , and 𝐸 are collinear. If 𝐴 𝐸 = 8 2 c m , 𝐵 𝐷 = 3 6 c m , and 𝐵 𝐶 = 𝐶 𝐷 = 𝐷 𝐸 , find the length of 𝐴 𝐷 .

Q10:

Suppose 𝑀 is the midpoint of 𝐹 𝐺 . Given that 𝑀 𝐺 = 2 𝑥 2 7 and 𝐹 𝐺 = 3 5 , find the value of 𝑥 .

Q11:

Find the length of 𝑋 𝑌 .

Q12:

Find the length of 𝑋 𝑌 .

Q13:

Find the length of 𝑋 𝑌 .

Q14:

Find the length of 𝑋 𝑌 .

Q15:

Find the length of 𝑋 𝑌 .

Q16:

Find the length of 𝑋 𝑌 .

Q17:

Find the length of 𝑋 𝑌 .

Q18:

Find the length of 𝑋 𝑌 .

Q19:

Find the length of 𝑋 𝑌 .

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