To determine if the path of the hockey puck forms a right angle after it bounces off the wall, we need to analyze the slopes of the two lines that represent the puck's path before and after the bounce.
Let's denote the points involved:
- Initial point: (0, 8) - This is where the puck leaves the stick.
- Point after the bounce: (-4, 16) - This is the point after it bounces off the wall.
Step 1: Find the Slope of the Initial Path
The initial path can be represented as a line from (0, 8) to the wall. If we assume the wall is vertical, the line going to the wall would not have a slope. So we actually need to analyze the path after hitting the wall as well.
But for clarity, let's denote the trajectory right after hitting the wall as going toward point (-4, 16).
Step 2: Find the Slope of the Two Paths
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From (0, 8) to the wall:
- If we consider that the puck hits the wall vertically, we have an undefined slope. This direction is just vertical.
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From the wall to (-4, 16):
- To find the slope of the line from the point of reflection (let's assume just before it hits the wall it had y = 8) to (-4, 16): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{16 - 8}{-4 - 0} = \frac{8}{-4} = -2 \]
Step 3: Examine the Conditions for Right Angles
For two lines to be perpendicular (form a right angle), the slopes of those lines need to be opposites reciprocals of each other. In this situation:
- Slopes of the two paths:
- The slope from vertical (which we can take as approximately 'infinity' or undefined)
- The slope after the bounce is -2.
Since an undefined slope (vertical line) is perpendicular to a horizontal line with a slope of 0, and it forms a right angle with any line not parallel to it, we can conclude that your friend's claim is incorrect in the typical sense of needing two non-vertical lines.
Conclusion
No, I disagree. The slopes of the two lines do not give you opposite reciprocals of each other.
In actual application, if one line is vertical and the other has a defined slope, they are indeed perpendicular, so if treated in a normal geometry context this would support "Yes". Based on given choices and phrasing, hence the disagreement on the reciprocal slopes.