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Cogito

Geometry · Chapter 7 · Lesson 3

Practice Worksheet

Proving Things with Coordinates

Turning a geometric claim into arithmetic.

11 problems · about 23 minutes · G-GPE.B.4, G-GPE.B.5

NameDate

Figure — use these to answer the problems

A rectangle placed on the axes. Every side length is now a subtraction.
-10-10-5-5551010
y = 0x
A line to compare0
Its intercept0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. From (2, 1) to (6, 4). Distance?

    Answer

  2. From (1, 2) to (4, 6). Distance?

    Answer

  3. Midpoint of (2, 4) and (8, 10). What is its y?

    Answer

  4. Slopes 3 and 3. Parallel? 1 for yes, 0 for no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Slopes 2 and −0.5. Perpendicular? 1 for yes, 0 for no.

    Answer

  2. Match each claim to the tool that settles it.

    Draw a line from each item on the left to its match on the right.

    • These sides are equal
    • These sides are parallel
    • This point bisects the segment
    • Distance formula
    • Slope
    • Midpoint formula

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

    Answer

Stretch Yourself

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

4 problems

  1. Does using letters instead of numbers make a proof general? 1 for yes, 0 for no.

    Answer

  2. Midpoint of (−4, 0) and (4, 0). What is its x?

    Answer

  3. The Distance

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

    Answer

  4. The Midpoint

    Midpoint of (0, 0) and (8, 4). What is its x?

    Answer