### Video Transcript

Determine the length of the
perpendicular from a point π΄ zero, zero to the line ππ₯ plus ππ¦ plus π equals
zero.

We donβt actually need a graph to
answer this question. But we can go ahead and make a
sketch. Hereβs a sketch. We have point π΄ at our origin. If this is the line ππ₯ plus ππ¦
plus π equals zero, then we could represent the perpendicular by this pink dotted
line. And thatβs the length weβre trying
to determine.

And we know something about the
perpendicular distance from a point to a line. Given the point π, π and ππ₯
plus ππ¦ plus π equals zero, the distance will be equal to the absolute value of
π΄ of π plus π΅ of π plus π over the square root of π΄ squared plus π΅
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 π times zero plus π
times zero plus π over the square root of π squared plus π squared. We know that π times zero plus π
times zero equals zero.

So weβll have the absolute value of
π divided by the square root of π squared plus π squared.