Video Transcript
Determine the length of the
perpendicular from a point 𝐴 zero, zero to the line 𝑎𝑥 plus 𝑏𝑦 plus 𝑐 equals
zero.
We don’t actually need a graph to
answer this question. But we can go ahead and make a
sketch. Here’s a sketch. We have point 𝐴 at our origin. If this is the line 𝑎𝑥 plus 𝑏𝑦
plus 𝑐 equals zero, then we could represent the perpendicular by this pink dotted
line. And that’s the length we’re trying
to determine.
And we know something about the
perpendicular distance from a point to a line. Given the point 𝑚, 𝑛 and 𝑎𝑥
plus 𝑏𝑦 plus 𝑐 equals zero, the distance will be equal to the absolute value of
𝐴 of 𝑚 plus 𝐵 of 𝑛 plus 𝑐 over the square root of 𝐴 squared plus 𝐵
squared. We have point zero, zero as our
start. And when we substitute what we
know, we get the distance is equal to the absolute value of 𝑎 times zero plus 𝑏
times zero plus 𝑐 over the square root of 𝑎 squared plus 𝑏 squared. We know that 𝑎 times zero plus 𝑏
times zero equals zero.
So we’ll have the absolute value of
𝑐 divided by the square root of 𝑎 squared plus 𝑏 squared.
