At what point does the line #(x+4)/2 = (y-6)/-1 = (z+2)/4# meet the coordinate planes?
2 Answers
Explanation:
While an untraditional definition of a line, we can try and break down what it is meaning.
In order to really define this line, I'm going to introduce a new variable
The "coordinate plane" refers to the traditional x-y plane. This has the property that z = 0. Hence, we can plug that in to find
Therefore,
Therefore, it intercepts the plane at
Explanation:
Given equation of line:
Let
Thus, there is a general point on the given line
Now, the line will intersect the XY-plane at the point where
hence, the point where the line intersects the XY-plane at the point
Now, the line will intersect the YZ-plane at the point where
hence, the point where the line intersects the YZ-plane at the point
Now, the line will intersect the ZX-plane at the point where
hence, the point where the line intersects the ZX-plane at the point