Coordinate Geometry with Triangles

Triangles Δ ABC and Δ A'B'C' are graphed in the standard (x,y) coordinate plane below. Triangle Δ A'B'C' is the image of Δ ABC under one of the following transformations. Which one?

• 90° clockwise rotation about the origin

• 90° counterclockwise rotation about the origin

• Horizontal translation

• Reflection across the x-axis

• Reflection across the y-axis

• Line

• Square

• Pentagon

• Parallelogram

• Scalene Triangle

If the figure is rotated 90 degrees clockwise, what are the coordinates of R?

• (-3, 3)

• (3, -3)

• (-3, -3)

• (3, 3)

Identify the transformation from A to D.

• 90^o Clockwise Rotation

• 180^o Rotation

• 270^o Clockwise Rotation

• 360^o Rotation

On the coordinate plane shown below, Figure G and Figure I are similar by a sequence of transformations. Which statement best describes the sequence of transformations from Figure G to Figure I?

• Figure G has been dilated to Figure H, which has been rotated to Figure I.

• Figure G has been rotated to Figure H, which has been translated to Figure I.

• Figure G has been reflected to Figure H, which has been dilated to Figure I.

• Figure G has been translated to Figure H, which has been reflected to Figure I.

Triangles ABC and A'B'C' are shown in the coordinate plane. Which statement describes a sequence of transformations that can be used to verify that triangle A'B'C' is similar to triangle ABC?

• Reflect triangle ABC across the x-axis, followed by a dilation with a scale factor of 2 about the origin.

• Reflect triangle ABC across the y-axis, followed by a dilation with a scale factor of 1/2 about the origin.

• Reflect triangle ABC across the x-axis, followed by a dilation with a scale factor of 1/2 about the origin.

• Reflect triangle ABC across the y-axis, followed by a dilation with a scale factor of 2 about the origin.

If the distances between points P, Q, and R are equal, which of the following could be true?

I. P, Q, and R are points on a circle with center O.

II. P and Q are points on a circle with center R.

III. P, Q, and R are vertices of an equilateral triangle.

• I only

• I and II only

• I and III only

• II and III only

• I, II, and III

Tags

G.9-12.3.A

Which transformation would take Figure K to Figure J?

• A reflection over the y-axis.

• A reflection over the x-axis.

Tags

G.9-12.3.C