Question

c use the graph to mark each statement as true or false. correct any false statements.
_____ 6. the pre - image is in quadrant iii.
_____ 7. the orientation of the vertices changed.
_____ 8. the reflection can be represented by (-x, y).
_____ 9. the line of reflection is the x - axis.
_____ 10. the pre - image and image are congruent.

Explanation:

Step 1: Analyze Statement 6

The pre - image (the original figure, ABCD) has vertices with negative x - coordinates and positive y - coordinates. Quadrant II is where \(x<0\) and \(y > 0\), not Quadrant III (\(x<0,y < 0\)). So the statement "The pre - image is in quadrant III" is False. The pre - image is in Quadrant II.

Step 2: Analyze Statement 7

For a reflection (in this case, likely over the x - axis or y - axis, but looking at the coordinates, the orientation of the vertices: in a reflection, if it's a reflection over the x - axis, the order of the vertices (the orientation) should remain the same (since reflection is a rigid transformation that preserves orientation in terms of the cyclic order of vertices for a polygon). So the statement "The orientation of the vertices changed" is False. The orientation remains the same.

Step 3: Analyze Statement 8

The reflection rule \((-x,y)\) is for reflection over the y - axis. Looking at the graph, the pre - image (ABCD) and image (\(A'B'C'D'\)): let's take a point, say \(A(-6,7)\), \(A'(-6,-7)\); \(B(-2,7)\), \(B'(-2,-7)\); \(C(-7,3)\), \(C'(-7,-3)\); \(D(-2,3)\), \(D'(-2,-3)\). The rule here is \((x,-y)\) (reflection over x - axis), not \((-x,y)\). So the statement "The reflection can be represented by \((-x,y)\)" is False. The correct rule is \((x, - y)\) (reflection over x - axis).

Step 4: Analyze Statement 9

Looking at the coordinates of the pre - image and image points: for a point \((x,y)\) in the pre - image, the image is \((x,-y)\). This is the rule for reflection over the x - axis. So the statement "The line of reflection is the x - axis" is True.

Step 5: Analyze Statement 10

Reflection is a rigid transformation. Rigid transformations (reflection, translation, rotation) preserve the shape and size of the figure, so the pre - image and image are congruent. So the statement "The pre - image and image are congruent" is True.

Answer:

s:

1. False (Pre - image is in Quadrant II)
2. False (Orientation remains same)
3. False (Reflection rule is \((x,-y)\) (over x - axis))
4. True
5. True