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

Q1:

Find the length of 𝑋 π‘Œ .

Q2:

Find the length of 𝑋 π‘Œ .

Q3:

Find the length of 𝑋 π‘Œ .

Q4:

Find the length of 𝑋 π‘Œ .

Q5:

Find the length of 𝑋 π‘Œ .

Q6:

Find the length of 𝑋 π‘Œ .

Q7:

Find the length of 𝑋 π‘Œ .

Q8:

Find the length of 𝑋 π‘Œ .

Q9:

Find the length of 𝑋 π‘Œ .

Q10:

Find the length of 𝑋 π‘Œ .

Q11:

Find the length of 𝑋 π‘Œ .

Q12:

If 𝐢 divides 𝐴 𝐡 by the ratio 4 ∢ 2 7 externally, find 𝐴 𝐢 𝐴 𝐡 and 𝐴 𝐡 𝐡 𝐢 .

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

Q13:

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

Q14:

If 𝐢 divides οƒ  𝐡 𝐴 by a ratio of 1 1 ∢ 2 5 internally, find 𝐴 𝐢 𝐡 𝐢 and 𝐴 𝐢 𝐴 𝐡 .

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

Q15:

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

Q16:

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

Q17:

𝐴 is the midpoint of 𝐡 𝐢 , where 𝐡 𝐴 = 1 0 π‘₯ βˆ’ 1 7 and 𝐴 𝐢 = 6 π‘₯ + 7 . Find π‘₯ and 𝐡 𝐢 .

  • A π‘₯ = 2 . 5 , 𝐡 𝐢 = 4 4
  • B π‘₯ = 6 , 𝐡 𝐢 = 4 3
  • C π‘₯ = 1 . 5 , 𝐡 𝐢 = 3 2
  • D π‘₯ = 6 , 𝐡 𝐢 = 8 6
  • E π‘₯ = 2 . 5 , 𝐡 𝐢 = 1 6

Q18:

Find the value of π‘₯ given 𝑂 𝐴 = 𝑂 𝐡 .

Q19:

Point 𝑄 is on the line between 𝑃 and 𝑅 . If 𝑃 𝑄 = 2 π‘₯ βˆ’ 3 , 𝑄 𝑅 = 4 π‘₯ + 8 , and 𝑃 𝑅 = 1 0 π‘₯ βˆ’ 5 , what is the length of 𝑃 𝑄 ?