Candice marked the points A, B, C, and D in this order on a straight line as shown in the diagram. The distance between A and C is 12 centimeters, and the distance between B and D is 18 centimeters. What is the distance between the midpoint of AB and the midpoint of CD? So first, let's assume that all these guys are on a number line, and we don't really care where they are on the number line, we just care that C-A has to be 12 and D-B has to be 18, because that's what we're given. So now we want the distance between the midpoint of AB and the midpoint of CD. The midpoint of AB lives at A plus B over 2, it's the average of A and B, and the midpoint of C and D lives at C plus D over 2, so we want the distance between these two quantities. Well that's just equal to C plus D over 2 minus A plus B over 2, then we just combine it together to get C minus A plus D minus B over 2. Well C minus A is 12, and D minus B is 18, so our final answer is 30 over 2 is 15, so it's A.

midpoint

distance

number line

geometry

calculation