What are the coordinates of the circumcenter of this triangle?

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a right triangle a b c is shown on a coordinate plane. a is located at begin ordered pair negative 3 comma 5 end ordered pair. b is located at begin ordered pair negative 2 comma negative 1 end ordered pair. c is located at begin ordered pair 8 comma negative 1 end ordered pair

The coordinates of the circumcenter of this triangle are (3,2)

Step-by-step explanation:

we know that

The circumcenter is the point where the perpendicular bisectors of a triangle intersect

we have the coordinates

step 1

Find the midpoint AB

The formula to calculate the midpoint between two points is equal to

substitute the values

step 2

Find the equation of the line perpendicular to the segment AB that passes through the point (-2,2)

Is a horizontal line (parallel to the x-axis)

-----> equation A

step 3

Find the midpoint BC

The formula to calculate the midpoint between two points is equal to

substitute the values

step 4

Find the equation of the line perpendicular to the segment BC that passes through the point (3,-1)

Is a vertical line (parallel to the y-axis)

-----> equation B

step 5

Find the circumcenter

The circumcenter is the intersection point between the equation A and equation B

-----> equation A

-----> equation B

The intersection point is (3,2)

therefore

The coordinates of the circumcenter of this triangle are (3,2)

(2,1) is the coordinates of the circumcenter of the triangle

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

it is x=-4

step-by-step explanation: