Describe Transformation Effects Using Coordinates - 8th Grade Math
Card 1 of 30
Identify the image of $P(-3,4)$ after translation by $(5,-2)$.
Identify the image of $P(-3,4)$ after translation by $(5,-2)$.
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$(2,2)$. Apply translation: $(-3+5, 4+(-2)) = (2,2)$.
$(2,2)$. Apply translation: $(-3+5, 4+(-2)) = (2,2)$.
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Which transformations always preserve distance (are rigid motions): translation, rotation, reflection, dilation?
Which transformations always preserve distance (are rigid motions): translation, rotation, reflection, dilation?
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Translation, rotation, and reflection. Only dilation changes distances; the others preserve them.
Translation, rotation, and reflection. Only dilation changes distances; the others preserve them.
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What is the coordinate rule for a $180^\circ$ rotation about the origin?
What is the coordinate rule for a $180^\circ$ rotation about the origin?
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$(x,y)\rightarrow(-x,-y)$. Negate both coordinates for half-turn around origin.
$(x,y)\rightarrow(-x,-y)$. Negate both coordinates for half-turn around origin.
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What is the coordinate rule for a $90^\circ$ clockwise rotation about the origin?
What is the coordinate rule for a $90^\circ$ clockwise rotation about the origin?
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$(x,y)\rightarrow(y,-x)$. Swap coordinates and negate new $y$ for $90°$ CW rotation.
$(x,y)\rightarrow(y,-x)$. Swap coordinates and negate new $y$ for $90°$ CW rotation.
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What is the coordinate rule for a $90^\circ$ counterclockwise rotation about the origin?
What is the coordinate rule for a $90^\circ$ counterclockwise rotation about the origin?
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$(x,y)\rightarrow(-y,x)$. Swap coordinates and negate new $x$ for $90°$ CCW rotation.
$(x,y)\rightarrow(-y,x)$. Swap coordinates and negate new $x$ for $90°$ CCW rotation.
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Identify the image of $(-2,5)$ after reflection across the line $y=x$.
Identify the image of $(-2,5)$ after reflection across the line $y=x$.
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$(5,-2)$. Swap coordinates: $(x,y)$ becomes $(y,x)$ across $y=x$.
$(5,-2)$. Swap coordinates: $(x,y)$ becomes $(y,x)$ across $y=x$.
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Identify the image of $(4,-1)$ after reflection across the $x$-axis.
Identify the image of $(4,-1)$ after reflection across the $x$-axis.
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$(4,1)$. Negate $y$-coordinate: $-1$ becomes $1$, $x$ stays $4$.
$(4,1)$. Negate $y$-coordinate: $-1$ becomes $1$, $x$ stays $4$.
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What is the coordinate rule for reflecting a point $(x,y)$ across the line $y=-x$?
What is the coordinate rule for reflecting a point $(x,y)$ across the line $y=-x$?
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$(x,y)\rightarrow(-y,-x)$. Swap and negate both coordinates for reflection across $y=-x$.
$(x,y)\rightarrow(-y,-x)$. Swap and negate both coordinates for reflection across $y=-x$.
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Identify the image of $(2,7)$ after a $90^\circ$ counterclockwise rotation about the origin.
Identify the image of $(2,7)$ after a $90^\circ$ counterclockwise rotation about the origin.
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$(-7,2)$. Apply rule: $(2,7) → (-7,2)$ by swapping and negating new $x$.
$(-7,2)$. Apply rule: $(2,7) → (-7,2)$ by swapping and negating new $x$.
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Identify the image of $(-6,3)$ after a $180^\circ$ rotation about the origin.
Identify the image of $(-6,3)$ after a $180^\circ$ rotation about the origin.
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$(6,-3)$. Negate both: $(-6,3) → (6,-3)$ for $180°$ rotation.
$(6,-3)$. Negate both: $(-6,3) → (6,-3)$ for $180°$ rotation.
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What is the coordinate rule for dilating a point $(x,y)$ by scale factor $k$ about the origin?
What is the coordinate rule for dilating a point $(x,y)$ by scale factor $k$ about the origin?
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$(x,y)\rightarrow(kx,ky)$. Multiply both coordinates by scale factor $k$.
$(x,y)\rightarrow(kx,ky)$. Multiply both coordinates by scale factor $k$.
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Identify the image of $(8,-4)$ after dilation about the origin with scale factor $\frac{1}{2}$.
Identify the image of $(8,-4)$ after dilation about the origin with scale factor $\frac{1}{2}$.
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$(4,-2)$. Multiply by $ rac{1}{2}$: $(8,-4) → (4,-2)$.
$(4,-2)$. Multiply by $ rac{1}{2}$: $(8,-4) → (4,-2)$.
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What is always true about side lengths after a dilation with scale factor $k$?
What is always true about side lengths after a dilation with scale factor $k$?
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Each length is multiplied by $|k|$. Dilation scales all distances by the absolute value of $k$.
Each length is multiplied by $|k|$. Dilation scales all distances by the absolute value of $k$.
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What happens to angle measures under translations, rotations, reflections, and dilations?
What happens to angle measures under translations, rotations, reflections, and dilations?
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Angles stay equal for all four transformations. All four transformations preserve angle measures.
Angles stay equal for all four transformations. All four transformations preserve angle measures.
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What is the coordinate rule for reflecting a point $(x,y)$ across the line $y=x$?
What is the coordinate rule for reflecting a point $(x,y)$ across the line $y=x$?
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$(x,y)\rightarrow(y,x)$. Swap coordinates to reflect across the diagonal line $y=x$.
$(x,y)\rightarrow(y,x)$. Swap coordinates to reflect across the diagonal line $y=x$.
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What is the coordinate rule for reflecting a point $(x,y)$ across the $y$-axis?
What is the coordinate rule for reflecting a point $(x,y)$ across the $y$-axis?
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$(x,y)\rightarrow(-x,y)$. Negate the $x$-coordinate to flip across the vertical axis.
$(x,y)\rightarrow(-x,y)$. Negate the $x$-coordinate to flip across the vertical axis.
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What is the coordinate rule for reflecting a point $(x,y)$ across the $x$-axis?
What is the coordinate rule for reflecting a point $(x,y)$ across the $x$-axis?
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$(x,y)\rightarrow(x,-y)$. Negate the $y$-coordinate to flip across the horizontal axis.
$(x,y)\rightarrow(x,-y)$. Negate the $y$-coordinate to flip across the horizontal axis.
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Identify the image of the point $(3,-2)$ after the translation $(x,y)\rightarrow(x-5,y+4)$.
Identify the image of the point $(3,-2)$ after the translation $(x,y)\rightarrow(x-5,y+4)$.
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$(-2,2)$. Apply the rule: $3-5=-2$ for $x$, $-2+4=2$ for $y$.
$(-2,2)$. Apply the rule: $3-5=-2$ for $x$, $-2+4=2$ for $y$.
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What is the coordinate rule for translating a point $(x,y)$ by $(a,b)$?
What is the coordinate rule for translating a point $(x,y)$ by $(a,b)$?
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$(x,y)\rightarrow(x+a,y+b)$. Add $a$ to $x$-coordinate and $b$ to $y$-coordinate to shift the point.
$(x,y)\rightarrow(x+a,y+b)$. Add $a$ to $x$-coordinate and $b$ to $y$-coordinate to shift the point.
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What is the coordinate rule for translating a point by $(a,b)$?
What is the coordinate rule for translating a point by $(a,b)$?
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$(x,y)\rightarrow(x+a,y+b)$. Add $a$ to $x$-coordinate and $b$ to $y$-coordinate to shift the point.
$(x,y)\rightarrow(x+a,y+b)$. Add $a$ to $x$-coordinate and $b$ to $y$-coordinate to shift the point.
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Identify the scale factor $k$ if $P(2,3)$ dilates about the origin to $P'(6,9)$.
Identify the scale factor $k$ if $P(2,3)$ dilates about the origin to $P'(6,9)$.
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$k=3$. Since $(2 cdot 3, 3 cdot 3) = (6,9)$, the scale factor is $3$.
$k=3$. Since $(2 cdot 3, 3 cdot 3) = (6,9)$, the scale factor is $3$.
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Identify the image of $P(7,-3)$ after a $180^\circ$ rotation about the origin.
Identify the image of $P(7,-3)$ after a $180^\circ$ rotation about the origin.
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$(-7,3)$. Negate both: $(7,-3) \rightarrow (-7,3)$
$(-7,3)$. Negate both: $(7,-3) \rightarrow (-7,3)$
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Identify the image of $P(5,-2)$ after dilation about the origin with $k=-3$.
Identify the image of $P(5,-2)$ after dilation about the origin with $k=-3$.
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$(-15,6)$. Multiply by $-3$: $(5 \cdot (-3), -2 \cdot (-3)) = (-15,6)$.
$(-15,6)$. Multiply by $-3$: $(5 \cdot (-3), -2 \cdot (-3)) = (-15,6)$.
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What is the coordinate rule for reflecting a point across the $x$-axis?
What is the coordinate rule for reflecting a point across the $x$-axis?
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$(x,y)\rightarrow(x,-y)$. Negate the $y$-coordinate while keeping $x$ unchanged.
$(x,y)\rightarrow(x,-y)$. Negate the $y$-coordinate while keeping $x$ unchanged.
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What is the coordinate rule for reflecting a point across the $y$-axis?
What is the coordinate rule for reflecting a point across the $y$-axis?
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$(x,y)\rightarrow(-x,y)$. Negate the $x$-coordinate while keeping $y$ unchanged.
$(x,y)\rightarrow(-x,y)$. Negate the $x$-coordinate while keeping $y$ unchanged.
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What is the coordinate rule for reflecting a point across the line $y=x$?
What is the coordinate rule for reflecting a point across the line $y=x$?
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$(x,y)\rightarrow(y,x)$. Swap the $x$ and $y$ coordinates.
$(x,y)\rightarrow(y,x)$. Swap the $x$ and $y$ coordinates.
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Identify the image of $P(6,-1)$ after reflection across the $x$-axis.
Identify the image of $P(6,-1)$ after reflection across the $x$-axis.
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$(6,1)$. Reflecting across $x$-axis negates $y$: $(6,-1)
ightarrow (6,1)$.
$(6,1)$. Reflecting across $x$-axis negates $y$: $(6,-1) ightarrow (6,1)$.
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Identify the image of $P(-2,5)$ after reflection across the $y$-axis.
Identify the image of $P(-2,5)$ after reflection across the $y$-axis.
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$(2,5)$. Reflecting across $y$-axis negates $x$: $(-2,5)
ightarrow (2,5)$.
$(2,5)$. Reflecting across $y$-axis negates $x$: $(-2,5) ightarrow (2,5)$.
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Identify the image of $P(3,-7)$ after reflection across the line $y=x$.
Identify the image of $P(3,-7)$ after reflection across the line $y=x$.
Tap to reveal answer
$(-7,3)$. Swap coordinates: $(3,-7)
ightarrow (-7,3)$.
$(-7,3)$. Swap coordinates: $(3,-7) ightarrow (-7,3)$.
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Identify the image of $P(2,-5)$ after a $90^\circ$ counterclockwise rotation about the origin.
Identify the image of $P(2,-5)$ after a $90^\circ$ counterclockwise rotation about the origin.
Tap to reveal answer
$(5,2)$. Apply rule: $(2,-5)
ightarrow (-(-5),2) = (5,2)$.
$(5,2)$. Apply rule: $(2,-5) ightarrow (-(-5),2) = (5,2)$.
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