Considering that the points A, B, C, and D are on the same line.
We know that C is the midpoint between A and B.
And B is between A and D.
First, let's sketch the points to visualize their positions:
The total length of the line AD is 15 units. Point B divides this line into two segments, AB and BD, so that:
[tex]AD=AB+BD[/tex]From this expression, you can calculate the measure of line segment AB:
[tex]\begin{gathered} AD=AB+BD \\ AB=AD-BD \\ AB=15-7 \\ AB=8 \end{gathered}[/tex]Next, if point C is the midpoint of AB, it means that it separates this segment into two equal segments AC and CB. We can calculate the length of these segments by dividing AB by 2:
[tex]\begin{gathered} AC=CB=\frac{AB}{2} \\ AC=CB=\frac{8}{2} \\ AC=CB=4 \end{gathered}[/tex]Now, what is left is to determine the length of the segment CD
Line segment CD is formed by the segments CB and BD, so that:
[tex]\begin{gathered} CD=CB+BD \\ CD=4+7 \\ CD=11 \end{gathered}[/tex]Line segment CD has a length of 11 units.
