Math 1 · Unit 11 · Lesson 1 · part 2 of 5
Three tools, and the ones you can count
Unit 4 ended by checking shapes with slopes, and said two tools were still missing: how long a segment is,...
Three tools, and the ones you can count
Unit 4 ended by checking shapes with slopes, and said two tools were still missing: how long a segment is, and where its middle is. This unit adds both. Three tools, three questions: how steep (slope), how long (distance), where is the middle (midpoint). With those three you can measure shapes and prove what kind of shape a set of points makes.
A segment is the straight piece between two points, its endpoints. Its distance is how long it is, always a positive number. Start with the segments you can count.
Same horizontal line
From (2, 3) to (9, 3): the y's are the same, so just count across. The x's differ by 9 − 2 = 7. Distance 7.
Same vertical line
From (4, −1) to (4, 5): the x's are the same, so count up. The y's differ by 5 − (−1) = 6. Distance 6.
Slanted
From (1, 2) to (4, 6): you cannot count along a slant. The squares on the grid do not line up with it. You need a trick.