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**Geometry Mini-Lesson (5, 3) (5, −3) (3, −5) (3, 5)**

Louis wants to create a figure that has line symmetry. He draws the figure along the line y = x, as shown below. What are the coordinates in the image of the point (5, 3) when his figure is reflected over the line y = x ? (5, 3) (5, −3) (3, −5) (3, 5) MA.912.G.3.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent.

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**Geometry Mini-Lesson (−6, −5) (−5, 6) (−6, 5) (6, −5)**

Selena drew the figure as shown. What are the coordinates in the image of the point (6, 5) when her figure is rotated 90 degrees counterclockwise about the origin? (−6, −5) (−5, 6) (−6, 5) (6, −5) MA.912.G.3.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent.

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Geometry Mini-Lesson Martina wants to create a quilt by sewing together individual polygons. Her favorite polygon is an octagon. Will Martina be able to tessellate the plane with a regular octagon to make a quilt? No. Martina can not tessellate a plane with any polygon with more than 6 sides. Yes. The sum of the interior angles is 1080°. This is a multiple of 360°, so Martina can tessellate the plane with a regular octagon. Yes. The interior angle of a regular octagon measures 180°. This is a factor of 360°, so Martina can tessellate the plane with a regular octagon. No. The interior angle of a regular octagon measures 135°. This is not a factor of 360°, so Martina cannot tessellate the plane with a regular octagon. MA.912.G.3.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent.

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**Geometry Mini-Lesson (−2, 6) (−3, 5) (−2, 5) (−3, 6)**

Juan is drawing a sketch of his neighborhood. All of the houses in his neighborhood are similar. Below is the sketch of Juan's neighborhood on the coordinate plane. The coordinates of the vertices H, O, U, S, and E all have integer values. Juan has begun to draw H'O'U'S'E'. What are the coordinates of vertex U' ? (−2, 6) (−3, 5) (−2, 5) (−3, 6) MA.912.G.3.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent.

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**Geometry Mini-Lesson (5, −2) (2, −5) (−5, −2) (5, 2)**

Trapezoid TRAP is shown on the coordinate grid below. The coordinates of vertices T, R, A, and P all have integer values. If trapezoid TRAP is rotated 270° counterclockwise about the origin to create trapezoid T'R'A'P', what will be the coordinates of T'? (5, −2) (2, −5) (−5, −2) (5, 2) MA.912.G.3.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent.

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**Geometry Mini-Lesson (−3, 1) (−1, 3) (1, 3) (−1, −3)**

Hexagon ABCDEF is shown below on a coordinate grid. The coordinates of vertices A, B, C, D, E, and F all have integer values. If hexagon ABCDEF is reflected about the line y = x to create hexagon A'B'C'D'E'F', what will be the coordinates of E' ? (−3, 1) (−1, 3) (1, 3) (−1, −3) MA.912.G.3.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent.

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Geometry Mini-Lesson Tom's favorite sport is soccer. He wants to create a tessellation for the background of his computer desktop that looks like a soccer ball. If a soccer ball is made of a regular pentagon surrounded by 5 regular hexagons, will Tom be able to tessellate the plane of his desktop to look like a soccer ball? Yes. The interior angle measure of a regular hexagon is 120°. Since this is a factor of 360°, Tom will be able to tessellate the plane of his desktop to look like a soccer ball. No. The interior angle measure of a regular pentagon is 108°. Since this is not a factor of 360°, Tom will not be able to tessellate the plane of his desktop to look like a soccer ball. No. The sum of one interior angle of a regular pentagon and one interior angle of a regular hexagon is 228°. Since this is not a factor of 360°, Tom will not be able to tessellate the plane of his desktop to look like a soccer ball. No. The sum of one interior angle of a regular pentagon and two interior angles of a regular hexagon is 348°. Since this is not a factor of 360°, Tom will not be able to tessellate the plane of his desktop to look like a soccer ball. MA.912.G.3.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent.

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Geometry Mini-Lesson MA.912.G.3.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent.

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Geometry Mini-Lesson MA.912.G.3.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent.

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