QuestionFigure is in Quadrant IV. After reflecting, rotating, and translating it, determine if these statements are true or false:
a. is in Quadrant II.
b. is in Quadrant III.
c. The -coordinates of are all negative.
d. The -coordinates of are all positive.
Initial position and shape of are needed.
Studdy Solution
STEP 1
Assumptions1. Figure is located in Quadrant IV.
. Figure is reflected across the -axis to form figure .
3. Figure is then rotated counterclockwise around the origin to form figure .
4. Figure is translated4 units to the left to form figure .
5. The initial position and shape of Figure in Quadrant IV, and whether Figure reaches or exceeds the origin (0,0) is unknown.
6. The shape of Figure (whether it's a point, line, or another shape) is unknown.
STEP 2
Since Figure is in Quadrant IV, it has positive -coordinates and negative -coordinates.
STEP 3
When Figure is reflected across the -axis to form Figure , the -coordinates change sign, but the -coordinates remain the same. Therefore, Figure has positive -coordinates and positive -coordinates, placing it in Quadrant I.
STEP 4
When Figure is rotated counterclockwise around the origin to form Figure , the -coordinates and -coordinates switch places and the sign of the new -coordinates changes. Therefore, Figure has negative -coordinates and positive -coordinates, placing it in Quadrant II.
STEP 5
When Figure is translated4 units to the left to form Figure , the -coordinates decrease by4. The -coordinates remain the same.
STEP 6
Now, let's evaluate each statementa. Figure is in Quadrant II.Since the -coordinates are negative and the -coordinates are positive, Figure is indeed in Quadrant II. Therefore, this statement is true.
b. Figure is in Quadrant III.
This statement is false. As per our assumption, Figure is in Quadrant IV.
c. The -coordinates for the vertices of are all negative.
Since Figure is in Quadrant II, where -coordinates are negative, this statement is true.
d. The -coordinates for the vertices of are all positive.
Since Figure is in Quadrant II, where -coordinates are positive, this statement is true.
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