Check?

In your own words, explain why we use the formula AB = |a - b| to find the distance of a segment. Include why you need to subtract and why you need to take the absolute value.

We use that formula |a-b| because a and b are representing coodinate numbers you need to subtract because if you add it you'll get a higher answer which wouldn't be right. you use the absolute value so when you get your answer and you count the spaces you go to the right direction not the wrong

pretty good, but

subtraction produces the difference between two values. The length of the line is the distance from one end to the other, or the difference between their values.

we take |a-b| because the length of a line segment is always a positive value. The direction does not matter.

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To find the distance of a segment using the formula AB = |a - b|, we first need to understand why we subtract the values and why we take the absolute value.

In geometry, "a" and "b" represent the coordinates of two points on a segment. Let's say point "a" is located at coordinate (x₁, y₁) and point "b" is at coordinate (x₂, y₂).

To measure the distance between these two points, we can subtract the values component-wise. This means subtracting the x-coordinates (x₂ - x₁) and the y-coordinates (y₂ - y₁). However, this alone wouldn't give us the correct distance.

The reason we take the absolute value (|a - b|) is to ensure that the result is always positive. Since distance is a scalar quantity and cannot be negative, we want to avoid any negative values that could arise from the subtraction. Taking the absolute value guarantees that we have a positive distance value.

Consider an example where point "a" is located at coordinate (2, 4) and point "b" is at coordinate (5, 6). If we subtract these values without taking the absolute value, we would get (-3, -2). This would suggest a negative distance, which doesn't make sense. By taking the absolute value, we eliminate the negative sign and obtain a positive distance value, which in this case is 3.

Therefore, by subtracting the coordinates and taking the absolute value, we correctly calculate the distance between two points on a segment. The formula AB = |a - b| ensures that the resulting distance is always positive and accurately represents the length of the segment.

Ask your teacher if you need help.