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To construct a circle that circumscribes to a triangle, you would have to construct a circle that where all vertices of the triangle are on the circle. To do this you would have to construct the perpendicular bisectors of each side with your compass and straight edge. Comment on this answer if you are unsure of how to construct a perpendicular bisect (it's a long fundamental process to describe, and I wouldn't want to lecture you one something you already know). Once you have done so, set your compass point on the point where all perpendicular bisectors intersect (they should intersect in ONE point, if not you will have to redo it). Set your other compass lead on one of the vertices and spin away! If you have done this correctly, you should hit all three vertices when spinning your compass. Hope this helps!
Fun fact: the point where all perpendicular bisectors intersect is called the circumcenter
Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.
-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b
The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.
