Question

An ant is crawling along a straight wire, which we shall call the x axis, from A to B to C to D (which overlaps A), as shown in the figure below. O is the origin. Suppose you take measurements and find that AB is 31 cm , BC is 12 cm , and AO is 7 cm .(Figure 1)

A. What is the ant’s position at point A?


B. What is the ant’s position at point B?


C. What is the ant’s position at point C?


D. What is the ant’s position at point D?

Answer 1

The ant's position at each point along the wire can be determined by calculating the total distance traveled from the starting point. At point A, the ant is 7 cm from the origin. At point B, the ant is 31 cm from the origin. At point C, the ant is 43 cm from the origin. At point D, the ant is 44 cm from the origin.

Step-by-step explanation:

The ant's position at point A is 7 cm from the origin along the x-axis. Since point A is the starting point, its position is simply the distance from the origin.

The ant's position at point B is the total distance traveled from A to B. Since the ant traveled 31 cm from A to B, its position at point B is 31 cm from the origin along the x-axis.

Similarly, the ant's position at point C is the total distance traveled from A to C. The ant traveled 31 cm from A to B and another 12 cm from B to C, so its position at point C is 43 cm from the origin along the x-axis.

Lastly, the ant's position at point D is the total distance traveled from A to D. The ant traveled 31 cm from A to B, another 12 cm from B to C, and it overlaps with A, so its position at point D is 44 cm from the origin along the x-axis.

Answer 2

Ants position at point A = -7 cm

Ants position at point B = 38 cm

Ants position at point C = 26 cm

Ants position at point D = -7 cm

Step-by-step explanation:

In this question, we are dealing with displacement which is the change in position of an object.

Now, we are told the journey began from A to B and then from C to D.

Now, AB = 31 cm and AO = 7cm

But along AB, we have the origin O.

Since A is on the left hand side of the origin, it means it is negative. Thus, position A = -7cm

Then position B = 31 - (-7) = 31 + 7 = 38 cm

Since BC = 12cm, then position C = 38 - 12 = 26 cm

Position D is same as position A = -7cm