Completing Grid Figures - ISEE Lower Level: Mathematics Achievement
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What is the image of $(2,5)$ after a $90^\circ$ counterclockwise rotation about the origin?
What is the image of $(2,5)$ after a $90^\circ$ counterclockwise rotation about the origin?
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$(-5,2)$. Applying the $90^\circ$ counterclockwise rotation rule transforms the point to its image.
$(-5,2)$. Applying the $90^\circ$ counterclockwise rotation rule transforms the point to its image.
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Identify the rule for a $90^\circ$ clockwise rotation about the origin of $(x,y)$.
Identify the rule for a $90^\circ$ clockwise rotation about the origin of $(x,y)$.
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$(y,-x)$. A $90^\circ$ clockwise rotation about the origin transforms $(x,y)$ to $(y,-x)$.
$(y,-x)$. A $90^\circ$ clockwise rotation about the origin transforms $(x,y)$ to $(y,-x)$.
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What point completes a square with vertices $(-1,-1)$, $(3,-1)$, and $(3,3)$?
What point completes a square with vertices $(-1,-1)$, $(3,-1)$, and $(3,3)$?
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$(-1,3)$. The fourth vertex completes the square by ensuring all sides are equal and angles are $90^\circ$.
$(-1,3)$. The fourth vertex completes the square by ensuring all sides are equal and angles are $90^\circ$.
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Identify the point symmetric to $A(2,-1)$ across the center point $M(5,3)$.
Identify the point symmetric to $A(2,-1)$ across the center point $M(5,3)$.
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$(8,7)$. The point symmetric across $M$ is calculated as $2M - A$, ensuring $M$ is the midpoint.
$(8,7)$. The point symmetric across $M$ is calculated as $2M - A$, ensuring $M$ is the midpoint.
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Identify the formula for the point $B(x_2,y_2)$ if $M(x_m,y_m)$ is the midpoint of $AB$ and $A(x_1,y_1)$ is known.
Identify the formula for the point $B(x_2,y_2)$ if $M(x_m,y_m)$ is the midpoint of $AB$ and $A(x_1,y_1)$ is known.
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$B(2x_m-x_1,2y_m-y_1)$. Rearranging the midpoint formula solves for $B$ when $M$ is the midpoint of $A$ and $B$.
$B(2x_m-x_1,2y_m-y_1)$. Rearranging the midpoint formula solves for $B$ when $M$ is the midpoint of $A$ and $B$.
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What is the midpoint of the segment with endpoints $(-2,5)$ and $(6,1)$?
What is the midpoint of the segment with endpoints $(-2,5)$ and $(6,1)$?
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$(2,3)$. The midpoint is calculated as the average of the x-coordinates and y-coordinates of the endpoints.
$(2,3)$. The midpoint is calculated as the average of the x-coordinates and y-coordinates of the endpoints.
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What is the reflection of the point $(4,-3)$ across the $x$-axis?
What is the reflection of the point $(4,-3)$ across the $x$-axis?
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$(4,3)$. Reflection across the x-axis negates the y-coordinate while keeping the x-coordinate unchanged.
$(4,3)$. Reflection across the x-axis negates the y-coordinate while keeping the x-coordinate unchanged.
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What is the reflection of the point $(-7,2)$ across the $y$-axis?
What is the reflection of the point $(-7,2)$ across the $y$-axis?
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$(7,2)$. Reflection across the y-axis negates the x-coordinate while keeping the y-coordinate unchanged.
$(7,2)$. Reflection across the y-axis negates the x-coordinate while keeping the y-coordinate unchanged.
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What is the slope of the line through $(1,2)$ and $(5,10)$?
What is the slope of the line through $(1,2)$ and $(5,10)$?
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$2$. Slope is calculated as the change in y divided by the change in x between the two points.
$2$. Slope is calculated as the change in y divided by the change in x between the two points.
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What is the fourth vertex of a parallelogram with consecutive vertices $A(-2,1)$, $B(1,4)$, $C(5,3)$?
What is the fourth vertex of a parallelogram with consecutive vertices $A(-2,1)$, $B(1,4)$, $C(5,3)$?
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$D(2,0)$. The fourth vertex of a parallelogram with consecutive vertices $A$, $B$, $C$ is found using $D = A + C - B$.
$D(2,0)$. The fourth vertex of a parallelogram with consecutive vertices $A$, $B$, $C$ is found using $D = A + C - B$.
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What is the fourth vertex of a parallelogram with $A(1,2)$, $B(5,2)$, and $C(6,6)$ consecutive?
What is the fourth vertex of a parallelogram with $A(1,2)$, $B(5,2)$, and $C(6,6)$ consecutive?
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$D(2,6)$. The fourth vertex of a parallelogram with consecutive vertices $A$, $B$, $C$ is found using $D = A + C - B$.
$D(2,6)$. The fourth vertex of a parallelogram with consecutive vertices $A$, $B$, $C$ is found using $D = A + C - B$.
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What is the image of $(6,-1)$ after a $180^\circ$ rotation about the origin?
What is the image of $(6,-1)$ after a $180^\circ$ rotation about the origin?
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$(-6,1)$. Applying the $180^\circ$ rotation rule transforms the point to its image.
$(-6,1)$. Applying the $180^\circ$ rotation rule transforms the point to its image.
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What is the image of $(-3,4)$ after a $90^\circ$ clockwise rotation about the origin?
What is the image of $(-3,4)$ after a $90^\circ$ clockwise rotation about the origin?
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$(4,3)$. Applying the $90^\circ$ clockwise rotation rule transforms the point to its image.
$(4,3)$. Applying the $90^\circ$ clockwise rotation rule transforms the point to its image.
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Identify the rule for a $180^\circ$ rotation about the origin of $(x,y)$.
Identify the rule for a $180^\circ$ rotation about the origin of $(x,y)$.
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$(-x,-y)$. A $180^\circ$ rotation about the origin transforms $(x,y)$ to $(-x,-y)$.
$(-x,-y)$. A $180^\circ$ rotation about the origin transforms $(x,y)$ to $(-x,-y)$.
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Identify the rule for a $90^\circ$ counterclockwise rotation about the origin of $(x,y)$.
Identify the rule for a $90^\circ$ counterclockwise rotation about the origin of $(x,y)$.
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$(-y,x)$. A $90^\circ$ counterclockwise rotation about the origin transforms $(x,y)$ to $(-y,x)$.
$(-y,x)$. A $90^\circ$ counterclockwise rotation about the origin transforms $(x,y)$ to $(-y,x)$.
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Identify the translation of $(x,y)$ by $(-5,4)$ in coordinate form.
Identify the translation of $(x,y)$ by $(-5,4)$ in coordinate form.
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$(x-5,y+4)$. Translation by a vector $(h,k)$ adds $h$ to the x-coordinate and $k$ to the y-coordinate.
$(x-5,y+4)$. Translation by a vector $(h,k)$ adds $h$ to the x-coordinate and $k$ to the y-coordinate.
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What point is $3$ units right and $2$ units down from $(-1,6)$?
What point is $3$ units right and $2$ units down from $(-1,6)$?
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$(2,4)$. Translating right adds to the x-coordinate, and down subtracts from the y-coordinate.
$(2,4)$. Translating right adds to the x-coordinate, and down subtracts from the y-coordinate.
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What is the reflection of the point $(3,-8)$ across the origin?
What is the reflection of the point $(3,-8)$ across the origin?
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$(-3,8)$. Reflection across the origin negates both the x-coordinate and y-coordinate.
$(-3,8)$. Reflection across the origin negates both the x-coordinate and y-coordinate.
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What point completes a rectangle with vertices $A(1,1)$, $B(1,5)$, and $C(6,5)$?
What point completes a rectangle with vertices $A(1,1)$, $B(1,5)$, and $C(6,5)$?
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$(6,1)$. The fourth vertex of the rectangle shares the x-coordinate with $C$ and the y-coordinate with $A$.
$(6,1)$. The fourth vertex of the rectangle shares the x-coordinate with $C$ and the y-coordinate with $A$.
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What point completes an axis-aligned rectangle with vertices $(-3,2)$, $(-3,-4)$, and $(5,-4)$?
What point completes an axis-aligned rectangle with vertices $(-3,2)$, $(-3,-4)$, and $(5,-4)$?
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$(5,2)$. The fourth vertex of an axis-aligned rectangle shares the x-coordinate of one point and y-coordinate of another to close the shape.
$(5,2)$. The fourth vertex of an axis-aligned rectangle shares the x-coordinate of one point and y-coordinate of another to close the shape.
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Identify the coordinate formula for the fourth parallelogram vertex $D$ when $A,B,C$ are consecutive.
Identify the coordinate formula for the fourth parallelogram vertex $D$ when $A,B,C$ are consecutive.
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$D=A+C-B$. For consecutive vertices $A$, $B$, $C$ in a parallelogram, the vector formula $D = A + C - B$ ensures parallel and equal sides.
$D=A+C-B$. For consecutive vertices $A$, $B$, $C$ in a parallelogram, the vector formula $D = A + C - B$ ensures parallel and equal sides.
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What point completes a square with vertices $(0,0)$, $(2,0)$, and $(2,2)$?
What point completes a square with vertices $(0,0)$, $(2,0)$, and $(2,2)$?
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$(0,2)$. The fourth vertex completes the square by maintaining equal side lengths and right angles with the given points.
$(0,2)$. The fourth vertex completes the square by maintaining equal side lengths and right angles with the given points.
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