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Flashcards: Rotations

What is the result of rotating the point $(2,\frac{1}{3})$ $\displaystyle (2,\frac{1}{3})$ about the origin in the plane by $180 \degree$ $\displaystyle 180 \degree$ ?

$(2,\frac{1}{3})$ $\displaystyle (2,\frac{1}{3})$

$(\frac{1}{3},2)$ $\displaystyle (\frac{1}{3},2)$

$(-2,-\frac{1}{3})$ $\displaystyle (-2,-\frac{1}{3})$

$(2,-\frac{1}{3})$ $\displaystyle (2,-\frac{1}{3})$

$(-2,\frac{1}{3})$ $\displaystyle (-2,\frac{1}{3})$

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Flashcards: Rotations

What is the result of rotating the point $(2,\frac{1}{3})$ $\displaystyle (2,\frac{1}{3})$ about the origin in the plane by $180 \degree$ $\displaystyle 180 \degree$ ?

$(2,\frac{1}{3})$ $\displaystyle (2,\frac{1}{3})$

$(\frac{1}{3},2)$ $\displaystyle (\frac{1}{3},2)$

$(-2,-\frac{1}{3})$ $\displaystyle (-2,-\frac{1}{3})$

$(2,-\frac{1}{3})$ $\displaystyle (2,-\frac{1}{3})$

$(-2,\frac{1}{3})$ $\displaystyle (-2,\frac{1}{3})$

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Flashcards: Rotations

What is the result of rotating the point $(2,\frac{1}{3})$ $\displaystyle (2,\frac{1}{3})$ about the origin in the plane by $180 \degree$ $\displaystyle 180 \degree$ ?

Your answer:

$(2,\frac{1}{3})$ $\displaystyle (2,\frac{1}{3})$

Your answer:

$(\frac{1}{3},2)$ $\displaystyle (\frac{1}{3},2)$

Your answer:

$(2,-\frac{1}{3})$ $\displaystyle (2,-\frac{1}{3})$

Your answer:

$(-2,\frac{1}{3})$ $\displaystyle (-2,\frac{1}{3})$

Correct answer:

$(-2,-\frac{1}{3})$ $\displaystyle (-2,-\frac{1}{3})$

Explanation:

Rotating a point

(x,y) $\displaystyle (x,y)$

geometrically in the plane about the origin $180\degree$ $\displaystyle 180\degree$ is equivalent to negating the coordinates of the point algebraically to obtain

(-x,-y) $\displaystyle (-x,-y)$ .

Thus, since our initial point was

$(2,\frac{1}{3})$ $\displaystyle (2,\frac{1}{3})$

we negate both coordinates to get

$(-2,-\frac{1}{3})$ $\displaystyle (-2,-\frac{1}{3})$

as the rotation about the origin by $180\degree$ $\displaystyle 180\degree$ .

Flashcards: Rotations

Nonagons

Examine the figures in the above diagram. Figure 2 is the result of performing which of the following transformations on Figure 1?

$84^{\circ }$ $\displaystyle 84^{\circ }$

$72^{\circ }$ $\displaystyle 72^{\circ }$

$48^{\circ }$ $\displaystyle 48^{\circ }$

$60^{\circ }$ $\displaystyle 60^{\circ }$

$36^{\circ }$ $\displaystyle 36^{\circ }$

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Flashcards: Rotations

Examine the figures in the above diagram. Figure 2 is the result of performing which of the following transformations on Figure 1?

Your answer:

$84^{\circ }$ $\displaystyle 84^{\circ }$

Your answer:

$48^{\circ }$ $\displaystyle 48^{\circ }$

Your answer:

$60^{\circ }$ $\displaystyle 60^{\circ }$

Your answer:

$36^{\circ }$ $\displaystyle 36^{\circ }$

Correct answer:

$72^{\circ }$ $\displaystyle 72^{\circ }$

Explanation:

The diagram below superimposes the two figures:

Nonagons

The transformation moves the black diagonal to the position of the red diagonal, and, consequently, points $\displaystyle A$ and $\displaystyle B$ to points $\displaystyle A'$ and $\displaystyle B'$ , respectively. This constitutes two-tenths of a complete turn clockwise, or a clockwise rotation of $\frac{2}{10} \times 360^{\circ } = 72^{\circ }$ $\displaystyle \frac{2}{10} \times 360^{\circ } = 72^{\circ }$

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Flashcards: Rotations

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