Geometry FLVS 03.04 Honors Segment One Activity Part C

The transformation of ∆DEF is described in the table. What are the coordinates of E' that will justify ∆DEF ~ ∆D'E'F'?

(6, 4)

Which transformation will result in an image that is congruent to its pre-image?

(x, y) → (−x, y)

After a dilation with a scale factor of 3 about the origin, ∆ABC maps onto ∆DEF. Which of the following statements is true?

3 · CA = FD

Which sequence of transformations will result in an image that is similar to its pre-image?

A reflection followed by a dilation

∆ABC was transformed according to the rule (x, y) → (x, −y) to create ∆A'B'C'. What transformation justifies the relationship between the triangles?

A reflection over the x-axis justifies ∆ABC ≅ ∆A'B'C'.

∆ABC was transformed according to the rule (x, y) → (−x, y) to create ∆A'B'C'. What transformation justifies the relationship between the triangles?

A reflection over the y-axis justifies ∆ABC ≅ ∆A'B'C'.

Triangle JKL is rotated 90° clockwise and then dilated by a scale factor of 4 centered at the origin. Which of the following statements describes the properties of triangles JKL and J''K''L'' after the transformations?

Corresponding sides are congruent after the rotation and proportional after the dilation.

Quadrilaterals LMNO and PQRS are shown in the figure. Are quadrilaterals LMNO and PQRS similar?

No, quadrilaterals LMNO and PQRS are not similar because their corresponding segments are not proportional.

∆PQR was reflected and then dilated by a scale factor of 4 to create ∆P''Q''R''. Which statement explains why ∆PQR is similar to ∆P''Q''R''?

Reflections and dilations preserve angle measure; therefore, the corresponding angles of ∆PQR and ∆P''Q''R'' are congruent.

Quadrilaterals LMNO and PQRS are shown in the figure. Are quadrilaterals LMNO and PQRS similar?

Yes, quadrilaterals LMNO and PQRS are similar because a reflection and a dilation map quadrilateral LMNO onto PQRS.

The vertices of ∆MNO and ∆PQR are described in the table. How can ∆MNO ~ ∆PQR be justified using rigid and non-rigid transformations?

∆MNO was dilated by a scale factor of 1/3 from the origin, then rotated 180 degree clockwise about the origin to form ∆PQR.

The vertices of ∆MNO and ∆PQR are described in the table. How can ∆MNO ~ ∆PQR be justified using rigid and non-rigid transformations?

∆MNO was dilated by a scale factor of 2 from the origin, then reflected over the y-axis to form ∆PQR.