Video: Finding the Length of the Perpendicular Line from a Point to the 𝑥-Axis

Find the length of the perpendicular from the point (−22, −5) to the 𝑥-axis.

01:41

Video Transcript

Find the length of the perpendicular from the point negative 22, negative five to the 𝑥-axis.

So to help us solve this problem, what I have done is I’ve drawn a bit of a sketch. So we’ve got our 𝑥-axis and our 𝑦-axis. Then I’ve also marked on the fact that we’ve got a point which is negative 22, negative five. Well, negative 22 is our 𝑥-coordinate and negative five is our 𝑦-coordinate. So now, let’s plot this point. So now, I’ve plot this point. So now, what do we want to do? We want to find the length of the perpendicular from that point. And we want that perpendicular to be to the 𝑥-axis.

Well, the 𝑥-axis is the horizontal axis. So in that case, what we want to find is the distance from our point to that horizontal axis. And we want the perpendicular. So, therefore, we want the direct distance from our point to this axis. Well, we know the 𝑦-coordinate of our point is negative five. So therefore, we know that it’s five units below the 𝑥-axis because, on the 𝑥-axis, 𝑦 is equal to zero.

So therefore, we can say that the length of the perpendicular from point negative 22, negative five to the 𝑥-axis is gonna be five length units. And yet I’ve shown that with a sketch. But as I said before, we could have worked it out without the sketch because if we’re looking for the perpendicular distance from the 𝑥-axis, well, this is just gonna be our 𝑦-coordinate, which, in this case, with negative five. So that tells us that it’s five units away from the 𝑥-axis.

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