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| <meta property="og:description" content="A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis."> | | <meta property="og:description" content="A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis."> |
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| <title>A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis.</title> | | <title>A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis.</title> |
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| <h3 id="back-link"><a href="../../#1.5">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#1.5">$\leftarrow$Back</a></h3> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <p> |
| $1.5.6.$ A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points $A$ and $B$ of this body are ($-1$, $2$) and ($3$, $1$), and the final position is ($-3$, $1$) and ($-2$, $-3$). Use a graphical plot to find the coordinates of the rotation axis. | | $1.5.6.$ A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points $A$ and $B$ of this body are ($-1$, $2$) and ($3$, $1$), and the final position is ($-3$, $1$) and ($-2$, $-3$). Use a graphical plot to find the coordinates of the rotation axis. |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| <p>Since the axis of rotation is fixed, all points of the body rotate around it and are perpendicular in direction. | | <p>Since the axis of rotation is fixed, all points of the body rotate around it and are perpendicular in direction. |
| </p> | | </p> |
| <p>If the coordinates of two points at the beginning and end are $A$, $B$ and $A'$, $B'$ respectively, then if you draw lines $AB$ and $A'B'$, their intersection point will be the center of rotation | | <p>If the coordinates of two points at the beginning and end are $A$, $B$ and $A'$, $B'$ respectively, then if you draw lines $AB$ and $A'B'$, their intersection point will be the center of rotation |
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| loading="lazy" width="350" /> | | loading="lazy" width="350" /> |
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| Intersection point of lines | | Intersection point of lines |
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| <p>According to constructions, this point has coordinates $(-3.4,\; 2.6)$ | | <p>According to constructions, this point has coordinates $(-3.4,\; 2.6)$ |
| </p> | | </p> |
| </p> | | </p> |
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| <h4>Answer</h4> | | <h4>Answer</h4> |
| <p> | | <p> |
| $(-3.4,\; 2.6)$ | | $(-3.4,\; 2.6)$ |
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