Don't understand how to solve this problem:
12. A, B, C, and D are points on a line, and the lengths of the line segments are: AB = 12, BC = 4, CD = 7, and DA = 15. Which of the following is a possible order for the points?
A.A,B,C,D
B. A,C,D,B
C. A,D,C,B
D. A,C,B,D
since AD=15 and AB=12, I'd say you have
A-12-B-3-D
Now, if C is 4 to the left of B, we have
A-8-C-4-B-3-D
So, choice (D)
To solve this problem, we can use the given information about the lengths of the line segments and determine the correct order for the points.
First, let's start with the point A. We know that AB = 12, so B must be 12 units away from A on the line.
Next, we can look at the length BC. Since BC = 4, C must be 4 units away from B.
Now, let's consider the length CD. CD = 7, so D must be 7 units away from C.
Finally, remember that A is also connected to point D. The length DA = 15, so D must be 15 units away from A.
Now, let's go through each of the given options and see if they match the distances we found:
Option A: A, B, C, D
From our findings, AB = 12, BC = 4, CD = 7, and DA = 15. This option satisfies all the given lengths, so it is a possible order for the points.
Option B: A, C, D, B
Following this order, AC = 16, CD = 7, and DB = 19, which do not match the given lengths. Thus, this option is not correct.
Option C: A, D, C, B
If we follow this order, AD = 22, DC = 7, and CB = 11, which do not match the given lengths. Therefore, this option is not correct.
Option D: A, C, B, D
Using this order, AC = 16, CB = 11, and BD = 3, which do not match the given lengths. Consequently, this option is not correct.
Based on our analysis, the only order that matches the given lengths is Option A: A, B, C, D.