Question

The endpoints of AB are A(–8, –6) and B(4, 10). The midpoint is at C(–2, 2). What is true about the point D, the midpoint of CB? Check all that apply.

The coordinates of D are (2, 6).
D partitions AB in a 2:1 ratio.
The coordinates of D are (1, 6).
C partitions AD in a 2:1 ratio.
D partitions AB in a 3:1 ratio.

Answer 1

True:
- The coordinates of D are (1, 6). (Midpoint of C(−2,2) and B(4,10) is ((−2+4)/2, (2+10)/2) = (1,6).)
- D partitions AB in a 3:1 ratio. (A + (3/4)(B−A) = D, so AD:DB = 3:1.)
- C partitions AD in a 2:1 ratio. (On AD, C is at 2/3 of the way from A to D, so AC:CD = 2:1.)

False:
- The coordinates of D are (2,6). (Incorrect.)
- D partitions AB in a 2:1 ratio. (Incorrect; it is 3:1.)