Experimental vs. Theoretical Probability Answers

A teacher asks students to determine the accuracy of this statement.A reflection over the x-axis and then over the y-axis results in the same transformation as a 180 rotation about the origin of the original figure.Kwame’s explanation of the accuracy of the statement is shown below.Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3). Step 2: Reflect the pre-image over the x-axis: (1, –2), (1, –4), (2, –3).Step 3: Reflect the figure from step 2 over the y-axis: (–1, 2), (–1, 4), (–2, 3).Step 4: Rotate the pre-image 180: (–1, –2), (–1, –4), (–2, –3).Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore the statement made by the teacher is inaccurate.Which best explains Kwame’s solution?

Figure G is rotated 90 clockwise about the origin and then reflected over the x-axis, forming figure H. Which sequence of transformations will produce the same results?

Angie’s rotation maps triangle XYZ to triangle X’Y’Z’. X(3, –6) maps to X’(–3, 6)Y(1, –2) maps to Y’(–1, 2)Z(–1, –5) maps to Z’(1, 5) Which describes the rotation?

Chareese reflects figure RSUT over the y-axis and then rotates the reflected figure 180 about the origin, resulting in figure A. She states that . Which best describes the accuracy of her congruency statement?

Which triangle is a translation of triangle X?

Triangle RST is translated 2 units left and then reflected over the y-axis. Which transformations of RST will result in the same image? Check all that apply.

Triangle QRS is rotated 180° about the origin.What are the coordinates of point S’?

Triangle GHI is rotated 90 clockwise and then reflected over the y-axis. Which congruency statement is true?

The diagram below shows several parking spots near the grocery store, formed with three parallel line segments and a transversal. If the measure of angle 4 is 132°, what is the measure of angle 7?

On a coordinate plane, point B(–6, 1) is translated to (–3, –2). Indira uses these steps to find a rule to describe the translation.Step 1Substitute the original coordinates and the translated coordinates into :Step 2Write two equations:Step 3Solve each equation:Step 4Write the translation rule:Which corrects Indira’s first error?

Parallel lines s and t are cut by a transversal, r, as shown. What is the value of x to the nearest whole number?

Which choice shows the coordinates of C’ if the trapezoid is reflected across the y-axis?

Triangle MNO is reflected over the x-axis and then translated up 4 and right 3. How can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position?

Jorge needs to reflect a figure across the line . Which statements are correct regarding steps he could take to complete the reflection? Check all that apply.

Which triangle is a translation of triangle P?

Point A has coordinate A(3, 2). The point is rotated 180° clockwise about the origin. What is the x-coordinate of point A’? ( enter one corrdinate point only )

Triangle XYZ is rotated 90° clockwise about the origin.What are the coordinates of point X’?

Tomaz realized that the tip of a second hand on a clock rotates about the center of the clock. He watched the second hand rotate around the center of the clock for 15 seconds. Which describes the rotation he observed?

The vertices A(–2, –1), B(–3, 2), C(–1, 3), and D(0, 0) form a parallelogram. The vertices A’(–1, –2), B’(2, –3), C’(3, –1), and D’(0, 0) are the image of the parallelogram after a sequence of transformations. Which sequence of transformations could produce the image from the pre-image?

What is the mapping rule for a 180 degree rotation about the origin?