Video: Finding the Distance between Given Points on the 𝑥-Axis

The given figure represents the number line of integers. Find the length of segment 𝐷𝐶 + length of segment 𝐹𝐵 considering that a length unit is 1 cm.

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Video Transcript

The given figure represents the number line of integers. Find the length of segment 𝐷𝐶 plus the length of segment 𝐹𝐵 considering that a length unit is one centimeter.

In order to find the length of segment 𝐷𝐶, we simply write 𝐷𝐶. We do not put the line segment above it. This represents the length. And in an order to find the length of a segment, we take the absolute value of the difference between the values of the starting point and the ending point.

So we start at 𝐷, which is negative three, and then we’re going to 𝐶, which is at negative two. And we’re supposed to find the difference between these. So we have the absolute value of three minus negative two.

Now if we subtract a negative, it will turn into a plus sign. So negative three plus two is equal to negative one. And the absolute value of any number makes it positive. So the absolute value of negative one is positive one, so the length of 𝐷𝐶 must be one centimeter.

Now let’s find the length of line segment 𝐹𝐵. So to find this length, we take the absolute value. We’re beginning at 𝐹, which is at negative one, and ending at 𝐵, which is positive one. And we find the difference between these. So negative one minus one is negative two, and the absolute value of negative two is positive two. So the length of segment 𝐹𝐵 is two centimeters.

And we are to find the sum of these lengths. So we have one centimeter plus two centimeters, which is equal to three centimeters. And this will be our final answer.

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