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Cogito

Integrated Math 1 · Chapter 7 · Lesson 1

Practice Worksheet

Distance and Midpoint

Measuring on a grid.

12 problems · about 21 minutes · G-GPE.B.7, G-GPE.B.6

NameDate

Figure — use these to answer the problems

The horizontal and vertical gaps are the legs. The distance between two points is the hypotenuse.
adjacent = 3opposite = 4hyp = 5
Horizontal gap3
Vertical gap4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. From (0, 0) to (8, 6). What is the distance?

    Answer

  2. Where does the distance formula come from?

    • The Pythagorean Theorem applied to the horizontal and vertical gaps.
    • It is an unrelated new formula.

  3. From (0, 0) to (3, 4). Distance?

    Answer

  4. From (0, 0) to (6, 8). Distance?

    Answer

  5. From (1, 1) to (1, 9). Distance?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. From (2, 6) to (10, 6). Midpoint x-coordinate?

    Answer

  2. From (3, 1) to (3, 11). Midpoint y-coordinate?

    Answer

  3. From (−2, 0) to (4, 0). Distance?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each operation by which formula uses it.

    Write each item under the heading it belongs to: Subtract the coordinates · Take a square root · Add the coordinates · Divide by 2

    Distance formula

    Midpoint formula

  2. From (0, 0) to (5, 12). Distance?

    Answer

  3. The Distance

    From (1, 2) to (4, 6). What is the distance?

    Answer

  4. The Middle

    From (2, 4) to (8, 10). What is the x-coordinate of the midpoint?

    Answer