Points Pand Q lie in plane A. How many lines contain P
1 answer:
Answer:
The correct answer is :
1. Line PQ (One line PQ).
Step-by-step explanation:
The first step to solve this question is to draw the plane A with the points P and Q lying on it.
We know that given two different points there is only one line that contains this two different points.
Let's analyze each option.
''2. Lines PQ and QP''
This option is wrong because there aren't two different lines. In fact it is only one line that can be named line PQ or line QP.
''3. The 2 lines PQ and QP plus another line that does not lie in plane A.''
This option is assuming that exist three lines that contain P and Q. This option is also wrong.
''1. Line PQ''
This option is correct. It will be clarify with the drawing I will attach.
''We can't name them all!''
This option is assuming that exist infinite lines that contain P and Q. This option is wrong.
In the drawing I call the line that contains P and Q as line L.
Given that P and Q lie in plane A necessarily the line L must lie on the plane A.
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The equation to derive the distance d is . The lengths of the other legs of the given triangle are (y2 - y1) and (x2 - x1).
Consider the two points (x1, y1) and (x2, y2)
The formula used for calculating the distance between the two points is
distance =
Given that,
The triangle in the graph has vertices (x1, y1), (x2, y2), and (x2, y1)
Since this triangle makes 90°, it is a right-angled triangle.
Hypotenuse = (x1, y1) to (x2, y2), Adjacent = (x1, y1) to (x2,y1), and Opposite = (x2, y1) to (x2, y2).
Consider the length of the hypotenuse = d
So, using the distance formula, the length of the hypotenuse(d) is,
And the lengths of the other two legs of the given triangle are,
Length of the adjacent side: (x1, y1) to (x2,y1)
=
=
=
Length of the opposite side: (x2, y1) to (x2, y2)
=
=
=
Therefore, the derived distances for the given triangle are:
, (x2 - x1), and (y2 - y1).
Learn more about the distance between two points here:
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