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•Math - Steve, Tuesday, July 22, 2014 at 7:36pm
ACBD
•Math - Henry, Tuesday, July 22, 2014 at 7:43pm
D. A,C,B,D.
•Math - mmv, Monday, June 22, 2015 at 3:57pm
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•Math - Steve, Tuesday, July 22, 2014 at 7:36pm
ACBD
•Math - Henry, Tuesday, July 22, 2014 at 7:43pm
D. A,C,B,D.
Can someone please explain how they got this answer? Thanks.
AB = 12, BC = 4, CD = 7, and DA = 15
Start off my assuming that the largest number is the whole line. That might not be so, but it's a good place to start.
B must be to the right of C, since BC < CD
That means we have ACBD.
Check:
AC=8
CB=4
BD=3
You just have to play around a bit.
To determine which order is possible for the points A, B, C, and D, we can look at the given lengths of the line segments.
Let's analyze each option:
A. A, B, C, D: If we follow this order, we have AB = 12, BC = 4, and CD = 7. The sum of these lengths would be 12 + 4 + 7 = 23. However, the problem states that CD = 7 and DA = 15, which means the sum of all four segments must be 12 + 4 + 7 + 15 = 38. Therefore, this option is not possible.
B. A, C, D, B: If we follow this order, we have AC = AB + BC = 12 + 4 = 16 and CD = 7. The sum of these lengths would be 16 + 7 = 23, which does not match the required sum of 38. Therefore, this option is not possible.
C. A, D, C, B: If we follow this order, we have AD = DA = 15 and DC = CD = 7. The sum of these lengths would be 15 + 7 = 22, which does not match the required sum of 38. Therefore, this option is not possible.
D. A, C, B, D: If we follow this order, we have AC = AB + BC = 12 + 4 = 16 and CB = CD + DA = 7 + 15 = 22. The sum of these lengths would be 16 + 22 = 38, which matches the required sum. Therefore, this option is possible.
Therefore, the correct answer is option D. A, C, B, D.
To determine which order is possible for the points A, B, C, and D on a line, we need to consider the lengths of the line segments AB, BC, CD, and DA given in the question.
Let's analyze the options one by one:
A. A,B,C,D: According to this option, the order of the points is A, B, C, and D. However, the question states that AB = 12, BC = 4, CD = 7, and DA = 15. With this information, we can see that AB + BC + CD is 12 + 4 + 7 = 23, which is greater than DA (15). Therefore, option A is not possible.
B. A,C,D,B: According to this option, the order of the points is A, C, D, and B. Now, let's analyze the lengths of the line segments. AC = AB + BC, which is 12 + 4 = 16, and CD = 7. If we add AC and CD, we get 16 + 7 = 23, which is equal to or greater than DA. So far, this order seems possible. However, the question states that AB = 12, and BC = 4, which implies that CB = BC = 4. Since the order in option B is C then B (CB), this would mean that CB and BC have different lengths, which contradicts the given information. So, option B is not possible.
C. A,D,C,B: According to this option, the order of the points is A, D, C, and B. Now, let's analyze the lengths of the line segments. AD = DA = 15, and DC = CD = 7. If we add AD and DC, we get 15 + 7 = 22, which is less than AB (12). Therefore, option C is not possible.
D. A,C,B,D: According to this option, the order of the points is A, C, B, and D. Now, let's analyze the lengths of the line segments. AC = AB - BC, which is 12 - 4 = 8, and CD = 7, and DA = 15. If we add AC, CD, and DA, we get 8 + 7 + 15 = 30, which is greater than BC (4). Therefore, option D is possible.
So, the correct answer is option D.