In how many ways can the line be named?Name them all
Answers
Answer:
Step 1 of 3
If different order implies different name, then the line l can be named using two points A and B in 2 ways; lineand line.
If different order implies different name, then the line l can be named using three collinear points A, B, and, C in 6 ways; line, line, line, line, lineand line.
If different order implies different name, then the line l can be named using four collinear points A, B, C, and, D in 12 ways;
line, line,
line, line,
line, line,
line, line,
line, line,
line, and line.
Therefore, in 12 ways the line l can be named using only these points A, B, C, and D, if different order implies different name.
Step 2 of 3
(b)
A plane can be named using any three non collinear points on the same plane.
Points A, B, C, D, and E, are coplanar points, so these points lie on the same plane.
No three points are collinear, so no three points lie on the same line.
Therefore, determine the number of different combinations of three letters (points) there are for the letters (points) A, B, C, D, and E.
Step 3 of 3
There will be as many planes as there are ways of selection of 3 points by the 5 points.
The first point can be selected in 5 ways; the second point can be selected in 4 ways; and the third point can be selected in 3 ways. Therefore, the numbers of ways of choosing 3 points are
Therefore, in 60 ways the plane can be named using only these points A, B, C, D, and E, if different order implies different name.
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answer
12 ways
Step-by-step explanation:
line line line line line and line .only these points ABCD if different order implies different name