Here are the solutions for each transformation problem. I have calculated the new coordinates for every point and identified the corresponding parts for you.
1) Translation: 4 units left and 6 units down
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Rule: Subtract 4 from the x-coordinate and subtract 6 from the y-coordinate $(x - 4, y - 6)$.
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Original Points: $L(3, 7)$, $M(0, 3)$, $K(4, 2)$.
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New Points:
* $L' = (3-4, 7-6) = (-1, 1)$
* $M' = (0-4, 3-6) = (-4, -3)$
* $K' = (4-4, 2-6) = (0, -4)$
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Corresponding Parts: Side $LM$ corresponds to $L'M'$, side $MK$ to $M'K'$, side $KL$ to $K'L'$. Angle $L$ corresponds to $L'$, $M$ to $M'$, $K$ to $K'$.
2) Translation: 1 unit left and 5 units down
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Rule: Subtract 1 from x and subtract 5 from y $(x - 1, y - 5)$.
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Original Points: $S(1, 4)$, $T(4, 5)$, $U(4, 0)$, $R(1, 1)$.
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New Points:
* $S' = (1-1, 4-5) = (0, -1)$
* $T' = (4-1, 5-5) = (3, 0)$
* $U' = (4-1, 0-5) = (3, -5)$
* $R' = (1-1, 1-5) = (0, -4)$
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Corresponding Parts: Sides $ST, TU, UR, RS$ correspond to $S'T', T'U', U'R', R'S'$. Angles correspond directly ($S \to S'$, etc.).
3) Rotation $90^{\circ}$ counterclockwise about the origin
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Rule: Swap coordinates and make the new x negative $(-y, x)$.
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Original Points: $X(1, 3)$, $Y(2, 4)$, $Z(4, 4)$, $W(1, 0)$.
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New Points:
* $X' = (-3, 1)$
* $Y' = (-4, 2)$
* $Z' = (-4, 4)$
* $W' = (0, 1)$
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Corresponding Parts: Side $XY$ corresponds to $X'Y'$, etc. Angles correspond directly.
4) Reflection across the y-axis
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Rule: Keep y the same, flip the sign of x $(-x, y)$.
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Original Points: $P(2, -3)$, $Q(4, -1)$, $R(5, -4)$.
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New Points:
* $P' = (-2, -3)$
* $Q' = (-4, -1)$
* $R' = (-5, -4)$
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Corresponding Parts: Side $PQ$ corresponds to $P'Q'$, etc. Angles correspond directly.
5) Reflection across the x-axis
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Rule: Keep x the same, flip the sign of y $(x, -y)$.
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Original Points: $J(-3, -1)$, $K(-4, 2)$, $L(-2, 3)$.
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New Points:
* $J' = (-3, 1)$
* $K' = (-4, -2)$
* $L' = (-2, -3)$
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Corresponding Parts: Side $JK$ corresponds to $J'K'$, etc. Angles correspond directly.
6) Rotation $90^{\circ}$ counterclockwise about the origin
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Rule: Swap coordinates and make the new x negative $(-y, x)$.
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Original Points: $D(1, 0)$, $E(3, 3)$, $F(4, 0)$.
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New Points:
* $D' = (0, 1)$
* $E' = (-3, 3)$
* $F' = (0, 4)$
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Corresponding Parts: Side $DE$ corresponds to $D'E'$, etc. Angles correspond directly.
Final Answer:
1) Plot points
$L'(-1, 1)$,
$M'(-4, -3)$, and
$K'(0, -4)$. Connect them to form the triangle.
2) Plot points
$S'(0, -1)$,
$T'(3, 0)$,
$U'(3, -5)$, and
$R'(0, -4)$. Connect them to form the quadrilateral.
3) Plot points
$X'(-3, 1)$,
$Y'(-4, 2)$,
$Z'(-4, 4)$, and
$W'(0, 1)$. Connect them to form the quadrilateral.
4) Plot points
$P'(-2, -3)$,
$Q'(-4, -1)$, and
$R'(-5, -4)$. Connect them to form the triangle.
5) Plot points
$J'(-3, 1)$,
$K'(-4, -2)$, and
$L'(-2, -3)$. Connect them to form the triangle.
6) Plot points
$D'(0, 1)$,
$E'(-3, 3)$, and
$F'(0, 4)$. Connect them to form the triangle.
*(Note: For all problems, label the angles with a single arc mark and the sides with a single tick mark to show they correspond to the original figure.)*
Parent Tip: Review the logic above to help your child master the concept of rigid transformation worksheet.
