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

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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:
-
Line AB:
-
Line AC:
-
Line AD:
-
Line BC:
-
Line BD:
-
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.