ISEE Lower Level Mathematics Achievement Flashcards: Completing Grid Figures

What this deck covers

This deck focuses on Completing Grid Figures, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Lower Level Mathematics Achievement.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the image of $(6,-1)$ after a $180^\circ$ rotation about the origin?

Answer: $(-6,1)$. Applying the $180^\circ$ rotation rule transforms the point to its image.

Flashcard 2: What is the image of $(2,5)$ after a $90^\circ$ counterclockwise rotation about the origin?

Answer: $(-5,2)$. Applying the $90^\circ$ counterclockwise rotation rule transforms the point to its image.

Flashcard 3: Identify the rule for a $90^\circ$ clockwise rotation about the origin of $(x,y)$.

Answer: $(y,-x)$. A $90^\circ$ clockwise rotation about the origin transforms $(x,y)$ to $(y,-x)$.

Flashcard 4: Identify the rule for a $180^\circ$ rotation about the origin of $(x,y)$.

Answer: $(-x,-y)$. A $180^\circ$ rotation about the origin transforms $(x,y)$ to $(-x,-y)$.

Flashcard 5: Identify the point symmetric to $A(2,-1)$ across the center point $M(5,3)$.

Answer: $(8,7)$. The point symmetric across $M$ is calculated as $2M - A$, ensuring $M$ is the midpoint.

Flashcard 6: What is the reflection of the point $(4,-3)$ across the $x$-axis?

Answer: $(4,3)$. Reflection across the x-axis negates the y-coordinate while keeping the x-coordinate unchanged.

Flashcard 7: What is the fourth vertex of a parallelogram with consecutive vertices $A(-2,1)$, $B(1,4)$, $C(5,3)$?

Answer: $D(2,0)$. The fourth vertex of a parallelogram with consecutive vertices $A$, $B$, $C$ is found using $D = A + C - B$.

Flashcard 8: What is the reflection of the point $(-7,2)$ across the $y$-axis?

Answer: $(7,2)$. Reflection across the y-axis negates the x-coordinate while keeping the y-coordinate unchanged.

Flashcard 9: What point completes an axis-aligned rectangle with vertices $(-3,2)$, $(-3,-4)$, and $(5,-4)$?

Answer: $(5,2)$. The fourth vertex of an axis-aligned rectangle shares the x-coordinate of one point and y-coordinate of another to close the shape.

Flashcard 10: Identify the rule for a $90^\circ$ counterclockwise rotation about the origin of $(x,y)$.

Answer: $(-y,x)$. A $90^\circ$ counterclockwise rotation about the origin transforms $(x,y)$ to $(-y,x)$.

Flashcard 11: Identify the translation of $(x,y)$ by $(-5,4)$ in coordinate form.

Answer: $(x-5,y+4)$. Translation by a vector $(h,k)$ adds $h$ to the x-coordinate and $k$ to the y-coordinate.

Flashcard 12: What is the fourth vertex of a parallelogram with $A(1,2)$, $B(5,2)$, and $C(6,6)$ consecutive?

Answer: $D(2,6)$. The fourth vertex of a parallelogram with consecutive vertices $A$, $B$, $C$ is found using $D = A + C - B$.

Flashcard 13: What point completes a square with vertices $(-1,-1)$, $(3,-1)$, and $(3,3)$?

Answer: $(-1,3)$. The fourth vertex completes the square by ensuring all sides are equal and angles are $90^\circ$.

Flashcard 14: What is the reflection of the point $(3,-8)$ across the origin?

Answer: $(-3,8)$. Reflection across the origin negates both the x-coordinate and y-coordinate.

Flashcard 15: Identify the coordinate formula for the fourth parallelogram vertex $D$ when $A,B,C$ are consecutive.

Answer: $D=A+C-B$. For consecutive vertices $A$, $B$, $C$ in a parallelogram, the vector formula $D = A + C - B$ ensures parallel and equal sides.

Flashcard 16: What point completes a square with vertices $(0,0)$, $(2,0)$, and $(2,2)$?

Answer: $(0,2)$. The fourth vertex completes the square by maintaining equal side lengths and right angles with the given points.

Flashcard 17: What is the slope of the line through $(1,2)$ and $(5,10)$?

Answer: $2$. Slope is calculated as the change in y divided by the change in x between the two points.

Flashcard 18: What is the midpoint of the segment with endpoints $(-2,5)$ and $(6,1)$?

Answer: $(2,3)$. The midpoint is calculated as the average of the x-coordinates and y-coordinates of the endpoints.

Flashcard 19: What point completes a rectangle with vertices $A(1,1)$, $B(1,5)$, and $C(6,5)$?

Answer: $(6,1)$. The fourth vertex of the rectangle shares the x-coordinate with $C$ and the y-coordinate with $A$.

Flashcard 20: What point is $3$ units right and $2$ units down from $(-1,6)$?

Answer: $(2,4)$. Translating right adds to the x-coordinate, and down subtracts from the y-coordinate.

Flashcard 21: What is the image of $(-3,4)$ after a $90^\circ$ clockwise rotation about the origin?

Answer: $(4,3)$. Applying the $90^\circ$ clockwise rotation rule transforms the point to its image.

Flashcard 22: 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.

Answer: $B(2x_m-x_1,2y_m-y_1)$. Rearranging the midpoint formula solves for $B$ when $M$ is the midpoint of $A$ and $B$.