I have a question that asks:
Give coordinates for a point that is $8$ units away from the line $y = 5$. Then find both points on the line $3x + 2y = 4$ that are $8$ units from the line $y = 5$.
So I don't really know how to go about doing this but I am having some thoughts regarding the fact that if the equation of the line is $y = 5$, then the $y$-coordinates for all of the points that the line will go through will be $5$.
And let's say if we have the coordinates of two points be $(x, y)$, then we can perhaps use the distance formula although I am not sure what I would use for the $x$-coordinate for the point that goes through line $y =$ $5$.
Can someone please help me with solving this problem? And please note that I am only in high school and haven't learned about these geometrical concepts so in-depth.
Best Answer
All the points which are $8$ units away from $y=5$ lie on parallels to that line with distance $8$, i.e. either on $y=5-8=-3$ or on $y=5+8=13$. Now intersect these two lines with the other line you have. I'll leave that to you as an exercise.