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Cogito

Geometry · Chapter 7 · Lesson 1

Practice Worksheet

Distance, Midpoint, and the Circle

Geometry done with coordinates.

10 problems · about 20 minutes · G-GPE.A.1, G-GPE.B.4, G-GPE.B.7

NameDate

Figure — use these to answer the problems

Move the point and think about its distance from the origin.
-10-10-5-5551010
(3, 4)
x3
y4
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Tangents and Chords”

    Radius 6, tangent 8. Distance to the centre?

    Answer

  2. From “Inscribed Angles”

    Central 90°. Inscribed on the same arc?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. From (2, 3) to (10, 9). Distance?

    Answer

  2. What is the distance formula really?

    • The Pythagorean theorem in coordinates.
    • A new formula to memorise.

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

    Answer

  4. From (1, 1) to (4, 5). Distance?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. From (3, 7) to (9, 11). Midpoint x-coordinate?

    Answer

  2. x² + y² = 49. What is the radius?

    Answer

Stretch Yourself

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

2 problems

  1. The Distance

    From (0, 0) to (3, 4). What is the distance?

    Answer

  2. The Midpoint

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

    Answer