Question

solve the problems below. be sure to show your thinking.

1. ben transformed a figure from quadrant iv to quadrant i. the pre - image and image are congruent figures, but the orientation of the figure changed. which could be the transformation ben used?

a. a rotation 90° counterclockwise
b. a dilation by a scale factor of 2
c. a translation up
d. a reflection over the y - axis

1. luke is going to reflect point r(6, 10) over the y - axis. what are the coordinates for r?

Explanation:

Step1: Analyze each transformation option for question 6

• Rotation 90° counter - clockwise: Rotating a figure from quadrant IV 90° counter - clockwise would move it to quadrant I, and congruent figures with changed orientation.
• Dilation by a scale factor of 2: Dilation changes the size of the figure, but the problem states pre - image and image are congruent (same size).
• Translation up: Translation is a slide, it does not change the orientation of the figure in terms of the quadrants in a way that would move from IV to I with orientation change.
• Reflection over the y - axis: Reflecting a figure over the y - axis from quadrant IV would move it to quadrant I, but orientation (left - right) changes.

Step2: Use the reflection rule for question 7

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((-x,y)\). Given the point \(R(6,10)\), when we reflect it over the \(y\) - axis, we change the \(x\) - coordinate sign. So \(x = 6\) becomes \(x=-6\) and \(y = 10\) remains the same.

Answer:

1. D. A reflection over the y - axis
2. \((-6,10)\)