Question

Finding the center of Gravity:

Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC.
Express your answers in centimeters, separated by commas.

Answer 1

The answer is:

xA = 0

XB = 0

XC = 10.0.

The explanation:

1) From the given figure we can see that the coin B lies at the origin with coordinates (0,0).

2) and the coins A, B and C  on the corners of a square.

3) The length of all sides in a square are equal. The distance between B and C form a side of a square.

4) So distance from B to C is 10 cm. Likewise, distance from B to A is also 10 cm.

5) and when B is located at point (0,0) and C is 10 units right of B, so coordinates of C will be (10,0).

6) A is located 10 units above B, so coordinates of A will be (0, 10).  

7) Therefore, the x-coordinates of A, B and C are 0,0 and 10 respectively.

Answer 2

The X-coordinate of the coin A is $\boxed{0\,{\text{cm}}}$, coin B is $\boxed{0\,{\text{cm}}}$ and coin C is $\boxed{10\,{\text{cm}}}$.

Further Explanation:

The three coins A, B , C are placed in the XY plane and they are placed along the X and Y axes. The X-coordinate of the coin is the value on X-axis at which they are placed.

The coin A is placed at the $10\,{\text{cm}}$ mark on the Y- axis and if we carefully look at its position along the X axis, then it will cross the X axis at the point $x = 0\,{\text{cm}}$. Therefore, the X-coordinate for the coin A is  $\boxed{{X_A} = 0\,{\text{cm}}}$.

Now, the coin B is placed as the intersection of the X and the Y axis. The point of intersection of the two axis in a 2-D plane is termed as the origin. It means that from this point, the plane starts. At origin the X as well as Y coordinates are zero.

Therefore, the X-coordinate for the coin is $\boxed{{X_B}=0\,{\text{cm}}}$.

The coin is placed at a distance of 10 cm from the coin B and it is placed along the X-axis. The X-coordinate of any point along the X-axis is the distance of the point from the origin. Therefore, the X-coordinate of the coin C is $\boxed{{X_C}=10\,{\text{cm}}}$.

Thus, the X-coordinate of the coin A is $\boxed{0\,{\text{cm}}}$, coin B is $\boxed{0\,{\text{cm}}}$ and coin C is $\boxed{10\,{\text{cm}}}$.

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Units and Measurements

Keywords:  Three identical coins, A, Band C, three corners of a square, 10cm on a side, X-coordinates, origin, distance from the origin, X-axis, Y-axis.