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If 4 points A, B, C and D are drawn on a paper. No three points are collinear. How many lines can be drawn through a maximum of two points?
No three points are collinear. So we can consider the points as the vertices of a quadrilateral. So 4 sides of a quadrilateral and 2 diagonals can be drawn. Therefore, 6 lines can be drawn in total.
If K is the midpoint of a line PQ, according to which axiom we can write \( KP = KQ = \frac{PQ}{2} \)?
According to axiom number 7, we can write as K is the midpoint of the line PQ.
If there are two lines AB and CD on a plane, then which of the following is correct?
As AB and CD lie on the same plane, they will intersect if they are not parallel and they will not intersect if they are parallel.
If the point K lies somewhere on the line segment AB, not on the end points, then which of the following is correct?
As it is not given that K is the midpoint of AB, it can lie anywhere on the line segment. So we can’t say that K is the midpoint. So we can write .
If five points A, B, C, D and E lies on a line such that C is the midpoint of AE, B is the midpoint of AC and D is the midpoint of CE, then which of the following is correct?
As C is the midpoint of AE, we can write AC = CE. B is the midpoint of AC and D is the mid point of CE, so we C is also the midpoint of BD. Now BC = CD.
(1)
How many points do two distinct lines have in common?
If the lines are parallel, they do not intersect. So they don’t have any common point. If lines intersect then they have one common point. So two distinct lines can have 0 or 1 common point.
How many line segments can be formed among 3 non collinear points?
The three points are non collinear. So we can draw 3 line segments.
Which of the following are the boundaries of the surfaces?
The lines are the boundaries of the surfaces.
If P, Q and R are three line segments on a plane, and the line segment P is parallel to line segment Q and line segment Q is parallel to the line segment R, then which of the following is correct?
If one line segment is parallel to two line segments then those are parallel to each other as well. Therefore, Line segment P and line segment R are also parallel.
Which of the following statement is incorrect?
The incorrect statement is that only one line passes through a particular point because infinite number of lines can pass through one particular point.