Now what we need is to use these two intersection points to create two more arcs down here. OK, so now these two arcs are the same distance from point A, because I kept one side of my compass on that point. And you need it to come below the line because you need to mark two arcs. OK, so see it opens up and comes down below the line. So I need to open this up a little bit, I think right about there, let me make sure. And you're going to want to open it up so that the compass is wider than the distance from the given point to the given line. When you're asked to construct perpendicular lines and you're given one of those lines and a point that's not on the line, here are the steps you're going to take to do that. We can say that this new line intersects the given line at a 90 degree angle, which means you've just created perpendicular lines. So go ahead and line up those points and there we go. And because we want the lines to be perpendicular, we want the lines to intersect at a 90 degree angle. Right there and right there and that line's going to go right through point A. Here are the two points that you need to create that perpendicular line. Remember, we want to make sure that they intersect. And I want to do the same thing to the intersection point over here on the right. And I'm going to swing an arc above, and then again below, point A. ![]() So let's go ahead and start here with the first one on the left. So if it's not open wide enough they may not intersect. You just want to make sure that it's wide enough so that when you create an arc up here from this intersection point and again from this one, that they intersect. And then you want to open the compass up a little bit more maybe. So you might want to just mark them off so you know where to put your compass exactly. Now what we want to do is use these two intersection points to create some more arcs above and below point A. We're going to do the same thing on the other side. So put your endpoint on A and swing that arc. ![]() You want to make sure that these arcs intersect. So it really doesn't matter what width your compass is at, as long as it's somewhere within the given line. And we're going to make some arcs that intersect the given line. This would mean that although the two lines may intersect they will not intersect at 90°.If you're asked to create perpendicular lines and you're given a line and a point that lies on that line, like point A here, here are the steps to do that.The first thing you want to do is grab your compass. If the negative reciprocal was not used his would mean that both lines would have a positive gradient, or they would both have a negative gradient. The reciprocal vs the negative reciprocalĪ common mistake is to state the gradient of the perpendicular to a line to be the reciprocal of the original gradient, and not the negative reciprocal.This is wrong because the equation is not in the form y = mx + c. Here, the value of the gradient could be incorrectly stated as 1 as the coefficient of x is 1. Write the equation of a line that is parallel to A.” Take example 1 again: “The equation of a line A is given as 5y = x − 10. ![]() If the equation of a straight line is not written with y as the subject, the gradient may not be correct so it is important to be confident with rearranging equations. The gradient is the coefficient of x, labelled as m. Not/incorrectly rearranging to the form y = mx + c.This will generate a new equation that looks like y = mx − 2 which is incorrect as it is the coefficient of x that remains the same, and the y-intercept changes. Write the equation of a line that is parallel to A.”Īfter making y the subject so we have the equation y=\fracx−2 the value for the gradient could be incorrectly taken as – 2. Take example 1: “The equation of a line A is given as 5y = x − 10. Using the y-intercept instead of the coefficient of x (parallel lines).
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