00:01
I have a circle with two points on the circle and a line going through those two points.
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I need to prove that the perpendicular bisector of line ab goes through the center of the circle, meaning it goes through the point zero zero.
00:20
In order to prove that the perpendicular bisector of ab goes through zero zero, i need to find the midpoint of a and b.
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And i need to find the slope of this line ab.
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So let's start with the midpoint.
00:41
To find the midpoint, i need to follow this formula.
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So let me label point a, x1, y1, and point b, x2, y2.
00:55
Let me stop the two my values.
00:57
X1 is 3 plus x2, 4, over, 2, y1, 4 plus y2, negative 3 over 2.
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If i simplify this, i'm gonna get 7 over 2 and 1.
01:29
Let me graph this point here.
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7 .5 is the same thing as 3 1 .2.
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3 and 1 .2.
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3 and a half.
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And then i had to go up 1.
01:39
So that point right there is the middle.
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Point.
01:44
Now let me find the slope of the line ab by following the formula.
01:54
Y2, negative 3 minus y1, 4 over x2, 4 minus 3, that equals negative 7 over 1, which is negative 7.
02:16
So the slope of this line.
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So the slope of this line is negative 7.
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Now i need to find the equation of the perpendicular bisector of this line.
02:27
In other words, a line that goes through this midpoint and when it intercepts the line ab, it forms 90 degree angles.
02:42
That will make it a perpendicular bisector...