Point A, B, and C all lie on a line. Point D is the midpoint of

Question

Point A, B, and C all lie on a line. Point D is the midpoint of AB and E is the midpoint of BC; AB = 4 and BC = 10. Which of the following could be the length of AE ? ​

(A) ​1

​(B) ​2 ​

(C) ​3 ​

(D) ​4 ​

(E) ​5

aarushi21 · Answer

shouldn't it be 9? ab+be=ae so 4+5?

Nabneet · Answer

A B C lie on a line.
Its not mandatory that C comes after B.

line can have points like . C______e_______A_____d____B

niks4472 · Answer

C_____E_A__D__B

AB = 4, AC = 10, => AC = 6

since E id mid CB => CE = 5, EA = CA-CE = 1

Sajjad1994 · Answer

OE

The “could be” language in the question signals that there are multiple possible arrangements for the points on the number line. Because BC is longer than AB, it might be the case that A is to one side of B and C or that A is between B and C.

Using the information about the midpoints (D and E) and the lengths of the line segments, fill in all of the remaining information for the two number lines.

The diagrams show that AE has two possible lengths, 1 and 9, however, only 1 appears in the answer choices, so (A) is the correct answer.

Answer: A

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Point A, B, and C all lie on a line. Point D is the midpoint of

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Point A, B, and C all lie on a line. Point D is the midpoint of

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