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Strategy 2: Translate from Words to a Figure or Diagram

To solve a problem in which a figure is described but not shown, draw your own figure. Draw the figure as accurately as possible, labeling as many parts as possible, including any unknowns.

Drawing figures can help in geometry problems as well as in other types of problems. For example, in probability and counting problems, drawing a diagram can sometimes make it easier to analyze the relevant data and to notice relationships and dependencies.

• This strategy is used in the following sample question.

This is a Multiple-Choice – Select One Answer Choice question.

  1. Which of the following numbers is farthest from the number 1 on the number line?

    (A) Negative 10
    (B) Negative 5
    (C) 0
    (D) 5
    (E) 10

     

    Explanation

    Circling each of the answer choices in a sketch of the following number line shows that of the given numbers, Negative 10 is the greatest distance from 1.

    The figure is a number line with 23 equally spaced tick marks labeled with the integers from negative 11 through positive 11. Going from left to right, the 5 evenly spaced integers negative 10, negative 5, 0, 5 and 10 are circled. The integer 1 is 1 tick mark to the right of 0. There is an arrow pointing to the integer 1.

    Another way to answer the question is to remember that the distance between two numbers on the number line is equal to the absolute value of the difference of the two numbers. For example, the distance between Negative 10 and 1 is The absolute value of negative 10 minus one, which equals 11 and the distance between 10 and 1 is The absolute value of 10 minus one, end absolute value, equals the absolute value of 9, which equals 9 The correct answer is Choice A, Negative 10