GRE® Coordinate Geometry Practice #3

This GRE quant practice question is a coordinate geometry problem solving question. Concepts tested: Distance formula and finding coordinates of points of trisection of a line segment using the section formula.

Question 3: Points C and D trisect the line segment joining points A(4, 5) and B (16, 14). What is the length of the line segment CD?

1. 15 units
2. 5 units
3. 10 units
4. 6 units
5. 3 units

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Video Explanation

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Explanatory Answer

Step 1 : Decode the Given data

C and D trisect the line segment AB.
Essentially, AC = CD = DB
Also, AC + CD + DB = AB
Therefore, CD = \\frac{\text{1}}{\text{3}})AB
Let us find the length of the segment AB using the distance formula. One third the length of AB is the length of CD.

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Step 2 : Find the length of CD

Length of AB = \\sqrt{{({x}_{2} - {x}_{1})}^{2} + {({y}_{2} - {y}_{1})}^{2}})
→ \\sqrt{{(16 - 4)}^{2} + {(14 - 5)}^{2}}) = \\sqrt{\text{225}}) = 15 units.

CD = \\frac{\text{1}}{\text{3}})AB = \\frac{\text{1}}{\text{3}}) × 15 = 5 units.

Choice B is the correct answer