To find the distance between the points (4, −2) and (4, −5), we can use the distance formula for points on a vertical or horizontal line. Since both points have the same x-coordinate (4), they are vertically aligned on the grid.
The distance between two points with the same x-coordinate can be calculated using the absolute difference of their y-coordinates:
Distance = |y2 − y1|
Here, \( y1 = -2 \) and \( y2 = -5 \).
So, the distance is:
Distance = |-5 - (-2)| = |-5 + 2| = |-3| = 3.
Now, looking at the options provided:
- None of the expressions explicitly match the direct calculation we performed. The correct way to express this scenario would be using the absolute difference formula between the y-coordinates.
However, the closest expression that might represent a form of the calculation is:
|−5| − |−2|
But this expression evaluates as:
|-5| = 5 and |-2| = 2
So, |−5| − |−2| = 5 - 2 = 3, which gives us the distance.
Thus, the correct response would be:
|−5| − |−2|.