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Lesson Worksheet: Partitioning a Line Segment on the Coordinate Plane Mathematics

In this worksheet, we will practice finding the coordinates of a point that divides a line segment on the coordinate plane with a ratio using the section formula.


If the coordinates of 𝐴 and 𝐵 are (5,5) and (1,4) respectively, find the coordinates of the point 𝐶 that divides 𝐴𝐵 internally by the ratio 21.

  • A(3,2)
  • B(1,1)
  • C(1,1)
  • D(1,1)


The coordinates of 𝐴 and 𝐵 are (1,9) and (9,9) respectively. Determine the coordinates of the points that divide 𝐴𝐵 into four equal parts.

  • A(9,5), (9,7), (4,2)
  • B(5,9), (7,9), (3,9)
  • C(5,9), (7,9), (7,5)
  • D(5,9), (7,9), (2,0)


If 𝐶𝐴𝐵 and 𝐴𝐵=3𝐶𝐵, then 𝐶 divides 𝐵𝐴 by the ratio .

  • A13
  • B31
  • C12
  • D21


A bus is traveling from city 𝐴(10,10) to city 𝐵(8,8). Its first stop is at 𝐶, which is halfway between the cities. Its second stop is at 𝐷, which is two-thirds of the way from 𝐴 to 𝐵. What are the coordinates of 𝐶 and 𝐷?

  • A(0,0), (3,3)
  • B(1,1), (2,2)
  • C(1,1), (4,4)
  • D(2,2), (2,2)


A quadrilateral has its vertices at the points 𝐴(5,3), 𝐵(0,2), 𝐶(2,6), and 𝐷(8,2). A point 𝐸 lies on 𝐴𝐶 such that the lengths of 𝐴𝐸 and 𝐶𝐸 are in the ratio of 12, and a point 𝐹 lies on 𝐵𝐷 such that the lengths of 𝐵𝐹 and 𝐷𝐹 are in the ratio of 13.

Find the coordinates of 𝐸.

  • A(3,3)
  • B(0,3)
  • C(0,4)
  • D(4,0)
  • E(0,1)

Find the coordinates of 𝐹.

  • A(4,2)
  • B(2,2)
  • C(6,2)
  • D(4,0)
  • E(2,0)

Find the slope of the line 𝐸𝐹.

Find the equation of the line 𝐸𝐹, giving your answer in the form 𝑦=𝑚𝑥+𝑐.

  • A𝑦=(𝑥+4)
  • B𝑦=𝑥+4
  • C𝑦=𝑥4+1
  • D𝑦=4𝑥4
  • E𝑦=𝑥+14


Line segment 𝐴𝐷 is a median in 𝐴𝐵𝐶, where 𝐴=(8,7) and 𝐷=(2,1). Find the point of intersection of the medians of the triangle 𝐴𝐵𝐶.

  • A(12,9)
  • B(4,3)
  • C(6,5)
  • D(18,15)


If 𝐴(3,2) and 𝐵(2,4), find the coordinates of point 𝐶 which divides 𝐴𝐵 externally in the ratio 43.

  • A(22,17)
  • B(17,22)
  • C(18,20)
  • D(17,22)


Consider points 𝐴(2,3) and 𝐵(4,3). Find the coordinates of 𝐶, given that 𝐶 is on the ray 𝐵𝐴 but NOT on the segment 𝐴𝐵 and 𝐴𝐶=2𝐴𝐵.

  • A(14,15)
  • B(0,1)
  • C(2,3)
  • D(8,9)


Points 𝐴, 𝐵, 𝐶, and 𝐷 have coordinates (15,7), (7,2), (4,17), and (13,2), respectively. 𝐸 is the midpoint of 𝐴𝐵, and 𝑀 divides 𝐶𝐷 externally by the ratio 74, find the length of 𝐸𝑀 to the nearest hundredth, considering a length unit =1cm.


Fill in the blank: Given that 𝐶(3,3) and 𝐷(4,2), the 𝑥-axis divides 𝐶𝐷 in the ratio .

  • A23
  • B32
  • C53
  • D35

This lesson includes 39 additional questions and 204 additional question variations for subscribers.

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