Absolute Value Notation?
Rewrite each statement using absolute value notation.
1. The number y is less than three units from the origin.
I don't understand this statement. I see the word origin and quickly think of the point (0,0), which has nothing to do with this exercise, right?
2. The sum of the distances of a and b from the origin is greater than or equal to the distance of a + b from the origin.
- SeanLv 52 months agoFavorite Answer
1) if the number is less than three units from the origin then it means the distance on the y axis is -3 < y < 3 which is |y| < 3
2) we have two numbers on the number line a and b. the statement says that the algebraic distance of a and of b is less than or equal to sum of the distances of the two from the origin.
a and -a are the same distance from the origin
b and -b are the same distance from the origin
the distance of the point (a+b) is |a+b|
distance from the origin of k = |k|
distance of a from the origin is |a|
distance of b from the origin is |b|
if a and b are on the same side of the origin
the distance of the point a+b
is |(a) + (b)| or |-(a) - (b) | which is
the same as |a|+|b|
if a and b are on opposite sides the total algebraic distance is
|a - b| or |b - a| = |a-b|
putting this together |a+b| is at most |a|+|b| and may be less |a-b|
- Anonymous2 months ago
Why do you think any of this problem must be 2
dimensional? if all problem are one-D, then
origin is just 0, not (0,0)
it says the number y is less than 3 units from the origin.
since it just says y , it may be one dimensional
y is less than 3 unit from y = 0
-3< y< 3
for y > 0 , y < 3
for y < 0 , y> -3
multiply both sides by
-1 and flip > to <
-y < 3 and y > 3 which is