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What are two lines that intersect on a plane at point O?
They are the x any y axes that are perpendicular to each other and intersect at zero on the Cartesian plane.
What is the longest a line segement a line or a ray?
In Geometry, a line is the longest between a line segment, a line and a ray. This is easy to determine given the definitions of each:-A line, which is determined by any two points in it, extends infinitely in both of its ends.-A line segment is the portion of a line contained between two points, including these points.-Any point O of a line divides it into two parts called rays that have a starting point in O but are infinite on their other end.So, a line segment is a segment with an end and a beginning, a ray has a beginning but not an end, and a line has no beginning or end, so a line is the longest.
The vertex of cod in the drawing above is point?
O the middle point! :)
Are a trapezoid's diagonals ever perpendicular?
Yes, they can be. Here is an example to see how this is true. Construct two perpendicular lines AB and CD that intersect at a point O. Let AO = CO, BO = DO and AO ≠ BO, then ABDC forms an isosceles trapezoid. If the lines are not perpendicular, then also ABDC is an isosceles trapezoid and it has perpendicular diagonals.
Is every point of an open set E contained in R2 a limit point of E?
In reply to "limit point", posted by Jennifer on Sept 24, 2004: >I have a basic question. Thanks a lot. > >Is every point of every open set E (is contained in R^2) a limit point of E? Yes, it is. If O is open and x is in O then some open ball B(x,e) is contained in O (as x is an interior point of O). But open balls in R^2 have the property that they contain many more points than just x (eg also (x_1 + 1/2*e, x_2) for x = (x_1, x_2), and e>0 ) and so if B(x,r) is any neighbourhood of x, then B(x, min(r,e)) will contain this point, which is in O (as B(x,e) \subset O) and not equal to x. So x is a limit point of O. >In case of for clsed sets in R^2? > There it fails, eg if C = {(1/n, 0): n in N}. No point of C is a limit point of C (but (0,0) is), as is easily checked. Henno
