Question

Point C is the midpoint of AB and point B is between points A and D. If AD = 15 and BD = 7, what is CD?

Answer 1

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:

`AD=AB+BD`

From this expression, you can calculate the measure of line segment AB:

`\begin{gathered} AD=AB+BD \\ AB=AD-BD \\ AB=15-7 \\ AB=8 \end{gathered}`

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:

`\begin{gathered} AC=CB=(AB)/(2) \\ AC=CB=(8)/(2) \\ AC=CB=4 \end{gathered}`

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:

`\begin{gathered} CD=CB+BD \\ CD=4+7 \\ CD=11 \end{gathered}`

Line segment CD has a length of 11 units.