Find the coordinates of the circumcenter of the triangle with the given vertices. X(-2, 1), Y(2, -3), Z(6, -3).
1 answer:
Answer:
C (4,3)
Step-by-step explanation:
Steps to find the circumcenter:
1) Find and Calculate the midpoint of given coordinates or midpoints.
2) Calculate the slope of the perpendicular bisector lines
3) By using the midpoint and the slope, find out the equation of the line
4) Do the same for another line
Solve the equations of two lines to get the intersection point.
The intersection point will be the circumcenter of the triangle.
Given :
X(-2,1), Y(2,-3), Z(6,-3)
Please see the attached file:
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Answer:
look below
Step-by-step explanation:
y = 2 (x + 3)^2 - 2
Geometric figure: parabola
Alternate forms:
y = 2 (x + 2) (x + 4)
y = 2 (x^2 + 6 x + 8)
-2 x^2 - 12 x + y - 16 = 0
Expanded form:
y = 2 x^2 + 12 x + 16
Roots:
x = -4
x = -2
<u>Properties as a real function: </u>
Domain - R (all real numbers)
Range - {y element R : y>=-2}
Partial derivatives:
d/dx(2 (x + 3)^2 - 2) = 4 (x + 3)
d/dy(2 (x + 3)^2 - 2) = 0
Implicit derivatives:
(dx(y))/(dy) = 1/(12 + 4 x)
(dy(x))/(dx) = 4 (3 + x)
Global minimum:
min{2 (x + 3)^2 - 2} = -2 at x = -3
