Explain why |−3| + |9| represents the distance between the points (−3, −5) and (9, −5).
The points are on a horizontal line, parallel to the x-axis. The absolute value of −3 represents the distance from (−3, −5) to the y-axis, and the absolute value of 9 represents the distance from the y-axis to (9, −5).
The points are on a horizontal line, parallel to the x-axis. The absolute value of -3 represents the distance from (-3,-5) to the y-axis, and the absolute value of 9 represents the distance from the y-axis to (9, -5).
Explain why |−3| + |9| represents the distance between the points (−3, −5) and (9, −5).
What is the distance between (12, –7) and (–3, –7)?
Ninja
To understand why |−3| + |9| represents the distance between the points (−3, −5) and (9, −5), let's break it down step by step.
First, recall that the absolute value of a number represents its distance from zero on a number line. The absolute value function removes the sign of the number and returns a positive value.
Now, let's consider the x-coordinates of the two points: −3 and 9. To find the distance between them, we need to subtract the smaller value from the larger value. In this case, 9 is greater than −3, so the absolute value of 9 minus (−3) will give us the distance between the x-coordinates: |9 - (−3)|.
Applying the subtraction, we have |9 - (−3)| = |(9 + 3)| = |12|.
Next, let's focus on the y-coordinates of the two points: −5 for both of them. Since the y-coordinates are the same, their difference is 0. Therefore, we do not need to consider the y-coordinate when calculating the distance.
Finally, let's put the x-coordinate and y-coordinate results together. The distance between the points (−3, −5) and (9, −5) is given by the formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Since the y2 and y1 terms cancel out as they are the same value, we're left with:
Distance = √((x2 - x1)^2 + 0^2)
= √((12)^2)
= √(144)
= 12
Therefore, |−3| + |9| represents the distance between the points (−3, −5) and (9, −5), which is 12.
|-3| = -(-3)
9-(-3) = 9+|-3|
but it's a stupid way to actually write it.