SOLUTION: Two vertices of a triangle are at (-6,5) and (9,-3). Find the locus of the third vertex if the area of the triangle is 85. So basically I got up to the point where the length o

Question 1068235: Two vertices of a triangle are at (-6,5) and (9,-3). Find the locus of the third vertex if the area of the triangle is 85.
So basically I got up to the point where the length of the base is 17, and the goal is to find locus of points 10 units away from exactly what I'm not sure. A fast response and complete response will be greatly appreciated!
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
If your two points give as a base, 17 units, (I did not check this) and the area is 85 square units, you should find that the height for your triangle is 10 units in length. Does that help you?

You are looking for any point which is 10 units distance from the LINE containing your chosen base. Equation of line containing the base with the given points as vertices is .

Look for a convenient point on the base's line. Is (-2,5) a point on this line? Is (3,-3) on the line?
Answer by ikleyn(52851) (Show Source): You can put this solution on YOUR website!
.
The locus of the third vertex is/are two parallel lines at the distance of 10 units from the given (base) line.

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