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What happens to the temperature and the density of the material between point b and c?
The answer depends on where points b and c are!
If S equals straight lines in the plane and ab if a and b are parallel Verify that the relation is an equivalence relation on the set S given?
Establishing equivalence depends on the definition of parallel lines. If they are defined as lines which cannot ever meet (have no point in common), then the relation is not reflexive and so cannot be an equivalence relation.However, if the lines are in a coordinate plane and parallel lines are defined as those which have the same gradient then:the gradient of a is the gradient of a so the relationship is reflexive ie a ~ a.if the gradient of a is m then b is parallel to a if gradient of b = m and, if the gradient of b is m then b is parallel to a. Thus the relation ship is symmetric ie a ~ b b ~ a.If the gradient of a is m then b is parallel to a if and only if gradient of b = gradient of a, which is m. Also c is parallel to b if and only if gradient of c = gradient of b which is m. Therefore c is parallel to a. Thus the relation is transitive, that is a ~ b and b ~ c => a ~ c.The relation is reflexive, symmetric and transitive and therefore it is an equivalence relationship.
How do you find a point that is collinear with four points?
The answer depends on the information that you have about the four points and the manner in which that information is presented. Suppose the 4 points are A, B, C and D and the point that you find is P. If you have the coordinates of A, B, C and D then gradient AP = gradient AB (or any other pair) will suffice. If you have any one of vectors AB (or AC, AD, BC, BD), then vector AP is parallel to vector AB will suffice.
What can you say about the graph Ax plus By equals C about the graph Ax plus By equals C?
It is a straight line with gradient -A/B and intercept C/B.
Is points B and C are collinear?
If points B and C are collinear, it means that they lie on the same straight line. To determine if points B and C are collinear, you would need to know the coordinates or have a visual representation of the points.
