Cogito
Grade 8 Math · Chapter 9 · Lesson 2
Distance Between Two Points
Pythagoras on a coordinate grid.
10 problems · about 19 minutes · 8.G.B.8
What this lesson teaches
The child finds the distance between two points using the Pythagorean theorem.
- Two points on a grid make a right triangle with the axes.
- The legs are the gaps in x and in y.
- The distance is the hypotenuse, found by Pythagoras.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — The Pythagorean Theorem: Legs 9 and 12. Hypotenuse?
Answer 15
Why 15.
Review — Placing an Irrational Number: √40 lies between which two whole numbers? Give the smaller.
Answer 6
Why Between 6 and 7.
Review — Cube Roots: Cube root of 216?
Answer 6
Why 6.
Warm Up
Straightforward practice. Get the method working first.
3 problemsFrom (0, 0) to (8, 15). Distance?
Answer 17
Why 17.
Legs 6 and 8. Distance?
Answer 10
Why 36 + 64.
From (1, 1) to (4, 5). Distance?
Answer 5
Why Legs 3 and 4.
Build It Up
The same ideas with more to keep track of.
2 problemsLegs 9 and 12. Distance?
Answer 15
Why 81 + 144.
From (−2, 0) to (1, 4). Distance?
Answer 5
Why Legs 3 and 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Diagonal: Legs of 3 and 4. What is the distance?
Answer 5
Why 5.
The Longer One: From (0, 0) to (5, 12). What is the distance?
Answer 13
Why 13.