How many lines through the origin make equal angles with the coordinate axes?
@Steve... Could u pls elaborate ?
To determine the number of lines through the origin that make equal angles with the coordinate axes, we can start by considering each coordinate axis individually.
For a line to make an equal angle with the x-axis, the line must be perpendicular to the x-axis. This means that the slope of the line must be equal to the negative reciprocal of the slope of the x-axis, which is 0. The equation of a line with a slope of 0 passing through the origin is y = 0.
Similarly, for a line to make an equal angle with the y-axis, the line must be perpendicular to the y-axis. In this case, the slope of the line must be equal to the negative reciprocal of the slope of the y-axis, which is undefined. The equation of a line with an undefined slope passing through the origin is x = 0.
Therefore, there are two lines passing through the origin that make equal angles with the coordinate axes: the x-axis (y = 0) and the y-axis (x = 0).