Dividing Segments Proportionately

New York State Common Core Math Geometry, Module 4, Lesson 12

Worksheets for Geometry

Student Outcomes

• Students find midpoints of segments and points that divide segments into 3, 4, or more proportional, equal parts.

Dividing Segments Proportionately

Classwork

Exercises

1. Find the midpoint of 𝑆𝑇 given 𝑆(−2, 8) and 𝑇(10,−4).
   
2. Find the point on the directed segment from (−2, 0) to (5, 8) that divides it in the ratio of 1: 3.

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3. Given 𝑃𝑄 and point 𝑅 that lies on 𝑃𝑄 such that point 𝑅 lies 7/9 of the length of 𝑃𝑄 from point 𝑃 along 𝑃𝑄:
   a. Sketch the situation described.
   b. Is point 𝑅 closer to 𝑃 or closer to 𝑄, and how do you know?
   c. Use the given information to determine the following ratios:
   i. 𝑃𝑅: 𝑃𝑄
   ii. 𝑅𝑄: 𝑃𝑄
   iii. 𝑃𝑅: 𝑅𝑄
   iv. 𝑅𝑄: 𝑃𝑅
   d. If the coordinates of point 𝑃 are (0, 0) and the coordinates of point 𝑅 are (14, 21), what are the coordinates of point 𝑄?
   
4. A robot is at position 𝐴(40, 50) and is heading toward the point 𝐵(2000, 2000) along a straight line at a constant speed. The robot will reach point 𝐵 in 10 hours.
   a. What is the location of the robot at the end of the third hour?
   b. What is the location of the robot five minutes before it reaches point 𝐵?
   c. If the robot keeps moving along the straight path at the same constant speed as it passes through point 𝐵, what will be its location at the twelfth hour?
   d. Compare the value of the abscissa (𝑥-coordinate) to the ordinate (𝑦-coordinate) before, at, and after the robot passes point 𝐵.
   e. Could you have predicted the relationship that you noticed in part (d) based on the coordinates of points 𝐴 and 𝐵?

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