42
Distance from a point to 0
Textbook: Part 2, lesson 42, pp. 10–12
GoalDistance from a point to 0: coordinate and unit segment.
New words
coordinate · koordinataunit segment · birlik kesmaorigin · boshlang‘ich nuqtadistance · masofa
Explanation
On a coordinate ray the origin O has coordinate 0. The unit segment is called e. The notation A(5) means that A is 5 unit segments from O, so OA = 5 e. If e = 3 cm, then OA = 5 × 3 = 15 cm. Conversely, dividing the distance by the unit segment gives the coordinate.
Worked examples
e = 4 cm, B(6): OB = 6 × 4 = 24 cm.
OC = 36 km and e = 4 km: the coordinate of C is 36 : 4 = 9, so C(9).
Class activity
“Measure the ray”: draw a ray with e = 1 cm, mark the points with coordinates 3, 7 and 12 and write their distances from O in centimetres.
Practice
1
On a ray e = 4 cm and the point is B(6). How many cm is OB?
24
2
OC = 36 km and the unit segment is e = 4 km. Find the coordinate of C.
9
3
e = 4 mm and the point is D(15). How many cm is OD? (10 mm = 1 cm)
6
4
The unit segment is e = 150 m and the point is K(7). How many m is it from O to K?
1050