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Point was transformed using the coordinate rule .
Match each image to its rule. Then, for each rule, decide whether it takes the original figure to a congruent figure, a similar figure, or neither. Explain or show your reasoning.
ARectangles R and R prime on coordinate plane. Both axes from negative 4 to 4. Rectangle R with vertices at 1 comma 1, 1 comma 2, 3 point 5 comma 1, 3 point 5 comma 2. Rectangle R prime with vertices at 1 comma negative 1, 2 comma negative 1, 1 comma negative 3 point 5, 2 comma negative 3 point 5.
Triangles F and F prime on coordinate plane. Both axes from negative 4 to 4. Triangle F, vertices at negative 2 comma 1, negative 1 comma 1, negative 2 comma 3. Triangle F prime, vertices at 2 comma 1, 4 comma 1, 4 comma 3.
CTriangles F and F prime on coordinate plane. Both axes from negative 4 to 4. Triangle F, vertices at 1 comma 1, 3 comma 1, 2 comma 3. Triangle F prime, vertices at negative 2 comma 0, negative 1 comma negative 2, negative 3 comma negative 2.
DGraph of triangles F and F prime. Vertices of F at 6 comma 4, 8 comma 4, and 6 comma 8. Vertices of F prime at 3 comma 2, 4 comma 2, 3 comma 4.
4 triangles on coordinate plane. Both axes from negative 10 to 10 by 2’s. Triangle A B C, vertices A at 2 comma 3, B at 5 comma 4, and C at 3 comma 4. Triangle A prime B prime C prime, vertices A prime at 2 comma 6, B prime at 5 comma 8, C prime at 3 comma 8. Triangle D E F, vertices D at negative 2 comma 1, E at negative 4 comma 3, F at negative 6 comma 1. Triangle D prime E prime F prime, vertices D prime at negative 2 comma negative 1, E prime at negative 4 comma negative 3, F prime at negative 6 comma negative 1.
Triangle has been transformed in two different ways:
Triangles A B C, D E F, and X Y C on coordinate plane. Horizontal x axis from negative 9 to 9. Vertical y axis from negative 12 to 6. Triangle A B C with vertices A at 2 comma negative 2, B at 3 comma negative 4 and C at 6 comma 0. Triangle D E F with vertices D at 2 comma 2, E at 4 comma 3 and F and 0 comma 6. Triangle X Y C with vertices X at 2 comma negative 6, Y at 3 comma negative 12, and C at 6 comma 0.
Let’s analyze the effects of the first transformation. If we calculate the lengths of all the sides, we find that segments and each measure units, and each measure 5 units, and and each measure units. The triangles are congruent by the Side-Side-Side Triangle Congruence Theorem. That is, this transformation leaves the lengths and angles in the triangle the same—it is a rigid transformation.
Not all transformations keep lengths or angles the same. Compare triangles and . Angle is larger than angle . All of the side lengths of are larger than their corresponding sides. The transformation stretches the points on the triangle 3 times farther away from the -axis. This is not a rigid transformation. It is also not a dilation since the corresponding angles are not congruent.