Question Video: Identifying the Distance between a Given Point and a Straight Line | Nagwa Question Video: Identifying the Distance between a Given Point and a Straight Line | Nagwa

# Question Video: Identifying the Distance between a Given Point and a Straight Line Mathematics • First Year of Secondary School

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Determine the length of the perpendicular from a point π΄(0, 0) to the line ππ₯ + ππ¦ + π = 0.

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### Video Transcript

Determine the length of the perpendicular from a point π΄ zero, zero to the line ππ₯ plus ππ¦ plus π equals zero.

We donβt actually need a graph to answer this question. But we can go ahead and make a sketch. Hereβs a sketch. We have point π΄ at our origin. If this is the line ππ₯ plus ππ¦ plus π equals zero, then we could represent the perpendicular by this pink dotted line. And thatβs the length weβre trying to determine.

And we know something about the perpendicular distance from a point to a line. Given the point π, π and ππ₯ plus ππ¦ 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 weβll have the absolute value of π divided by the square root of π squared plus π squared.

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