Question

1. a shape is shown below. which shows this shape transformed by a flip? a. b. c. d. 11. which of the following is a single reflection of figure n over the y - axis to form n? a. b. c. d.

Explanation:

Step1: Understand the concept of reflection (flip)

A reflection (flip) over a line (in problem 11, the \(y -\)axis) changes the position of a figure such that each point of the original figure has a corresponding point on the reflected figure at the same distance from the line of reflection but on the opposite side. For a reflection over the \(y -\)axis, the rule for a point \((x,y)\) in the original figure \(N\) is that its image in \(N'\) is \((-x,y)\). This means that the \(y -\)coordinate of each point remains the same, and the \(x -\)coordinate is the opposite of the original \(x -\)coordinate. In problem 10, a flip (reflection) changes the orientation of the shape with respect to a line (not shown in the general shape problem, but conceptually, it's a mirror - like transformation).

Step2: Analyze problem 10

In problem 10, when we flip (reflect) a shape, it's like looking at it in a mirror. Option C shows the correct mirror - like transformation of the given shape. If we consider the orientation of the "indent" in the shape, in the original shape, the indent is on the left - lower part. After a flip (assuming a vertical flip line in a general sense for the non - coordinate - based problem), the indent should be on the right - lower part, which is what option C shows.

Step3: Analyze problem 11

In problem 11, for a reflection over the \(y -\)axis:

• Look at the position of figure \(N\) and its image \(N'\). In option A, if we consider the general position of the figures with respect to the \(y -\)axis, the \(x -\)coordinates of the points of \(N\) and \(N'\) are opposites (\(x\) and \(-x\)) while the \(y -\)coordinates are the same. For example, if a point in \(N\) has a positive \(x -\)coordinate (right of the \(y -\)axis), its image in \(N'\) has a negative \(x -\)coordinate (left of the \(y -\)axis) with the same \(y -\)coordinate.

Answer:

1. C.
2. A.