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Distances, routes and shapes on the plane

الأسبوع 25 · المسافات على المستوى الإحداثي ورسم الأشكال من نقاط · 3 دروس
1

Distance between two points on a horizontal or vertical line

Discover Mathematics P6: Term 2, Unit 11, Lessons 4–6
GoalFind the distance between two points on a horizontal or a vertical line using absolute values.
New words
distance · how far apart two points are, always a positive numberabsolute value · the distance of a number from 0; |−4| = 4horizontal / vertical · left–right / up–down
Explanation

When two points have the same y-coordinate they lie on a horizontal line, and we compare their x-coordinates. When they have the same x-coordinate they lie on a vertical line, and we compare their y-coordinates. Use absolute values, which are the distances from 0. If the two numbers are on the SAME side of 0 (both positive or both negative), subtract the absolute values: the bigger minus the smaller. If they are on OPPOSITE sides of 0, add the absolute values, because the distance goes through 0. The distance between (−3, 2) and (4, 2) is 3 + 4 = 7. The distance between (−7, 1) and (−2, 1) is 7 − 2 = 5.

The two numbersWhat to doExample
Same side of 0subtract the absolute values|−7| − |−2| = 5
Opposite sides of 0add the absolute values|−3| + |4| = 7
Worked examples
xy−6−5−4−3−2−1123456−6−5−4−3−2−11234560AB
A(−3, 2) and B(4, 2) have the same y, so the segment is horizontal. A is 3 left of the y-axis and B is 4 right of it. Opposite sides, so AB = 3 + 4 = 7 units.
C(−7, 1) and D(−2, 1) are on a horizontal line and both x-values are negative (same side). CD = 7 − 2 = 5 units.
E(2, 5) and F(2, −4) have the same x, so the segment is vertical. E is 5 above the x-axis and F is 4 below it. EF = 5 + 4 = 9 units.
Class activity

Number line walk. Draw a number line from −10 to 10 on the floor with chalk or tape. Stand on two numbers and count the steps between you. Check with absolute values.

Practice
1
Find the distance between (−6, 3) and (2, 3).
2
Find the distance between (5, −2) and (5, 7).
3
Find the distance between (−9, 0) and (−4, 0).
4
Find the distance between (0, 8) and (0, −3).
5
Hana says the distance between (−5, 4) and (3, 4) is 5 − 3 = 2. What is wrong? What is the distance?