The points A, B, C, D, and E are located on a straight line in order. The distance from A to E is 20cm. The distance from A to D is 15cm. The distance from B to E is 10cm. C is halfway between B and D. Find the distance from A to C.: *
2.5 cm
5 cm
10 cm
12.5 cm
Draw a sketch and think it through, one statement at a time.
The first tells you that the total length is 20 cm.
The second tells you that D is 5 cm from the the right end (E).
The third tells you that B is 10 cm from each end (and in the middle). The fourth tells you where to put C
etc
To find the distance from A to C, we need to first find the distance from A to D and then subtract half of the distance from D to B.
Given that the distance from A to D is 15 cm, and C is halfway between B and D, we can conclude that the distance from D to C is equal to the distance from C to B.
Since the distance from B to E is given as 10 cm, we can infer that the distance from C to B is half of that, which is 10 cm divided by 2, resulting in 5 cm.
Now, we can find the distance from A to C by subtracting half of the distance from D to B (which is 5 cm) from the distance from A to D (which is 15 cm):
Distance from A to C = Distance from A to D - Distance from C to B
= 15 cm - 5 cm
= 10 cm
Therefore, the distance from A to C is 10 cm.
To find the distance from A to C, we can use the concept of proportions. Since C is halfway between B and D, we can say that the distance from B to C is equal to the distance from C to D. Let's call this distance x cm.
The distance from B to E is 10 cm, which means the distance from B to D is 10 cm + x cm.
Now, since the points A, B, C, D, and E are located on a straight line, we can add up the distances to find the total distance from A to E.
The distance from A to E is the sum of the distances from A to D and D to E:
Distance from A to E = Distance from A to D + Distance from D to E
= 15 cm + (10 cm + x cm)
We know that the distance from A to E is 20 cm, so we can set up an equation:
15 cm + (10 cm + x cm) = 20 cm
Simplifying this equation, we get:
25 cm + x cm = 20 cm
Subtracting 20 cm from both sides, we get:
x cm = -5 cm
Since we are dealing with distances, we cannot have a negative value. Therefore, there is no solution to this equation.
Thus, we cannot determine the distance from A to C based on the given information.