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
Here,
AE[20cm] - AD[15cm] = DE [5cm]
BE[10cm] - DE[5cm] = BD [5cm]
BC = CD = 2.5 cm.
so, AC = AD[15cm] - CD[2.5cm] = 12.5cm.
-----------------------------------------------------------------------------------
A B C D E
To find the distance from A to C, we need to first find the distances between different points.
1. Since C is halfway between B and D, the distance from B to C would be equal to the distance from C to D.
2. Let's assume the distance from B to C is x cm. Since C is halfway between B and D, C to D would also be x cm. Now we have the distances B to C = x cm and C to D = x cm.
3. Since A, B, C, D, and E are located on a straight line, the distance from A to E is the sum of the distances from A to D and D to E. Thus, A to E = A to D + D to E.
4. We're given that A to E is 20 cm and A to D is 15 cm. Substituting these values, we have 20 cm = 15 cm + D to E.
5. By subtracting 15 cm from both sides, we get D to E = 5 cm.
6. Finally, B to E is given as 10 cm.
Now we have all the information needed to find the distance from A to C:
A to C = A to B + B to C = (A to E − B to E) + (B to C)
= (20 cm - 10 cm) + (x cm)
= 10 cm + x cm.
Since we know B to C = C to D = x cm and D to E = 5 cm, we can substitute these values into the equation:
10 cm + x cm = (B to C) + (C to D) + D to E
10 cm + x cm = x cm + x cm + 5 cm
10 cm + x cm = 2x cm + 5 cm.
To solve for x, we can subtract 5 cm and 10 cm from both sides:
x cm = (10 cm + x cm - 5 cm) / 2
x cm = (5 cm + x cm) / 2.
Simplifying further, we get:
2x cm = 5 cm + x cm
x cm = 5 cm.
Now we can find the distance from A to C:
A to C = 10 cm + x cm
= 10 cm + 5 cm
= 15 cm.
Therefore, the distance from A to C is 15 cm.