The question doesn't say what the shape is, but it certainly looks like a triangle RST. It's also possible that the three points are on the same line and R is the midpoint, which would be ((-4-7)/2,(-6-3)/2)=(-5.5,-4.5).
If it's a right triangle, there's insufficient information to find R, because many triangles would fit, and the right-angled vertex of all possible right triangles would describe a semicircle with the given points as the diameter. If the right angle is at either of the given points, R could be anywhere.
If it's an isosceles triangle, there's insufficient information to find R.
If RS is the hypotenuse of an isosceles right triangle, then we can find two sets of coordinates for R.
The line RS has a slope=(3-(-6))/(-7-(-4))=3/-3=-1. This is the tangent of 45°, measured as a backward slope, and since a right triangle has 2 angles of 45°, RS must be at the same y value as either S (RS is horizontal) or T (RT is horizontal), and at the same x value as either T (RT is vertical) or S (RS is vertical), respectively. This means that R is either (-7,-6) or (-4,-3) respectively.
Another possibility is that RST is an equilateral triangle. This is more difficult to calculate but, again R has two possible coordinates because the apex could be on either side of the line RS. R would be either ( -5.5+1.5√3,-4.5+1.5√3) or (-5.5-1.5√3,-4.5-1.5√3).
Please clarify your question.
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