If B is the midpoint of AC, and C is the midpoint of BD, then what percent of CD is AC?
A. 25%
B. 50%
C. 100%
D. 200%
HELP
Is it A, 25%?
Nope. (D)
Did you draw a diagram?
Do so, and label the points. You will have 3 equal sections: AB,BC,CD.
AC is twice as long as CD.
Oh thanks. I actually thought it was 33% because there were 3 pieces
To determine what percent of CD is AC, we can use the concept of proportions.
Let's start by assigning values to the segments AC and CD. Since B is the midpoint of AC, we can say that AB = BC, and since C is the midpoint of BD, we can say that CD = 2 * BC.
Let's assume that AC has a value of "x". Therefore, BC would also be "x" since B is the midpoint of AC. And CD would be 2 * BC, which would be 2 * x.
So, AC = x and CD = 2 * x.
To find the percent of CD that is AC, we can set up the proportion:
(AC / CD) * 100 = (x / 2x) * 100
Simplifying this expression, we get:
(AC / CD) * 100 = (1/2) * 100
AC / CD = 1/2
This means that AC is half the length of CD. In other words, AC is 50% of CD.
Therefore, the correct answer is B. 50%.
To determine the percent of CD that AC represents, we need to compare the length of AC to the length of CD.
Given that B is the midpoint of AC, we know that AB and BC are equal in length. Similarly, since C is the midpoint of BD, CD and BC are equal in length.
Let's assign a variable to the length of AC, for example, let AC = x. Since B is the midpoint of AC, we know AB = BC = x/2.
Now let's consider the length of CD. Since C is the midpoint of BD, we know CD = BC = x/2.
To find the percent of CD that AC represents, we need to find the ratio of AC to CD:
AC/CD = (x)/(x/2) = 2.
This means that AC is twice as long as CD. So the correct answer is:
D. 200%