To solve this problem, we first need to determine the slopes of the lines defined by points W, X and Y, Z to check if they are indeed parallel.
Step 1: Finding the slope of Line 1 (points W and X)
Points W(-1, 3) and X(-3, 5) are used to calculate the slope (m) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
For points W and X:
- \( (x_1, y_1) = (-1, 3) \)
- \( (x_2, y_2) = (-3, 5) \)
Calculating the slope: \[ m = \frac{5 - 3}{-3 - (-1)} = \frac{2}{-2} = -1 \]
Step 2: Finding the slope of Line 2 (points Y and Z)
Points Y(-3, 6) and Z(-6, 9) are used in the same manner:
For points Y and Z:
- \( (x_1, y_1) = (-3, 6) \)
- \( (x_2, y_2) = (-6, 9) \)
Calculating the slope: \[ m = \frac{9 - 6}{-6 - (-3)} = \frac{3}{-3} = -1 \]
Both lines have the same slope of -1, confirming that they are parallel as expected.
Step 3: Identifying the quadrants of the transformed points
Assuming that transformations are made (translations, reflections, dilations, etc.), and without specifics on the transformations, we will consider the original locations of points:
- Point W(-1, 3) is in Quadrant II (negative x, positive y).
- Point X(-3, 5) is in Quadrant II (negative x, positive y).
- Point Y(-3, 6) is in Quadrant II (negative x, positive y).
- Point Z(-6, 9) is in Quadrant II (negative x, positive y).
Summary of Points:
All original points W, X, Y, and Z are located in Quadrant II.
Step 4: Will image W'X' be parallel to image Y'Z'?
Since the transformations (assuming they keep the parallelism intact) will not change the geometry of the figures (parallel lines remain parallel), the image of W'X' will also be parallel to Y'Z'.
Conclusion:
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Quadrants for W', X', Y', Z': All points will be in Quadrant II after the transformation (if it preserves the properties).
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Parallelism: Yes, W'X' will be parallel to Y'Z'.
Now you can check the desired boxes based on the answers above.
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