Question
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onsider the points , and . Which two
aes determined by these points are perpendicular? Explain.

Ask by Salinas Goodwin. in the United States
Jan 15,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The lines AC and BD are perpendicular because their slopes are negative reciprocals of each other.

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The Deep Dive

To determine which of the four lines defined by the points , , , and are perpendicular, we first need to find the slopes of the lines.
The formula for the slope between two points and is given by:
Calculating the slopes:
  1. Line AB:
  2. Line AC:
  3. Line AD:
  4. Line BC:
  5. Line BD:
  6. Line CD:
Next, we identify pairs of slopes that are negative reciprocals of each other, as this indicates that the lines are perpendicular (i.e., ).
Checking pairs:
  • and : Not perpendicular.
  • and : Not perpendicular.
  • and : Not perpendicular.
  • and : Not perpendicular.
  • and : Not perpendicular.
  • and : These are indeed negative reciprocals ( ).
Thus, the lines determined by points A and C with point B and D are perpendicular!
So, the answer is: Lines AC and BD are perpendicular.

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