About geometric place. To get an equation that satisfies the geometric place of the P(x,y) point, what's the first step? The equation is in the form y=mx+b, but it has to be at equal distance from point (2,1) to (-4,3)
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Question

About geometric place. To get an equation that satisfies the geometric place of the P(x,y) point, what's the first step? The equation is in the form y=mx+b, but it has to be at equal distance from point (2,1) to (-4,3)
?

anonymous · Answer

One solution would be any straight line parallel to a line through the two points.

liliakarina · Answer

@wsgalinaitis I just have to calculate the distance between the points and then the eq?

anonymous · Answer

So, when I read this question I think I understand what you are asking, however, I will restate  it. To begin, Let's solve for the mid point of the segment that has endpoints (2,1) and (-4,3). First, 
$$Distance = \sqrt{(x_2-x_1)^2-(y_2-y_1)^2}$$
Secret hint, the midpoint of two points is the sum of the components and then divided by 2. This means that the midpoint M is 
$$((-4+2)/2,1+3)/2)=(-1,2)$$
Now check that with the distance equation and you will see that they are equidistant apart.

anonymous · Answer

If you would like I can prove it generally that the midpoint will always be the sum of the components divided by 2, all we do is replace x1 with $$x_1=(x_2+x_1)/2$$ And the same with y1. This will give you the original distance over 2 after you take the 4 out of the square root.

anonymous · Answer

Now, If you want a line passing through the point (2,1) and (-4,3), we need to find the slope, m. This means we use the equation $$m=Rise/Run=(y_2-y_1)/(x_2-x_1)$$ and so our slope is -6/2=-3

anonymous · Answer

just plug this back into the equation y=mx+b and using m=3, (x=2,y=1) and  solve for b. and you have your answer.