 Krishna
0

Step 1: Name those given vertices and recall "what is a circumcenter"

NOTE: The circumcenter is the point of intersection of the axes that passes

perprendicularly trough the midpoint of a side of that traingle.

A=(−3,−3), B=(5,1), C=(11,−1).

Step 2: Calculate the midpoints of the sides

NOTE: Note down the endpoints (x_1, y_1) and (x_2, y_2) from the given

points. And substitute the values into the midpoint formula.

[FORMULA: The midpoint formula is

M = \left(\frac{\left(x_1+x_2\right)}{2},\frac{\left(y_1+y_2\right)}{2}\right)

where M is the midpoint of a line segment with endpoints at

(x_1, y_1) and (x_2, y_2).

Step 3: Find the line perpendicular to side (AB) that passes through mid-point

FORMULA: Equation of the line

(y - y_1) = m (x - x_1)

Slope m = \frac{y_2 - y_1}{x_2 - x_1}

NOTE: Two lines with slopes m_1and m_2 are perpendicular if

m_1* m_2 = -1

Step 4: In the same way calculate the line perpendicular to another side (BC) that    passes through mid-point.

Step 5: Solve the two equations to find the intersection point of the two perpendicular lines of the triangle sides.

EXAMPLE:  y = −2x + 1

y = 3x − 24

Solve the equations for x.  L.H.S are equal so equate the R.H.S

−2x + 1 = 3x − 24

x = 5

x=5, plugging it in y= −2x + 1

y = -2 (5) + 1

y = -9

So, Circumcenter  = (x, y) = (5, -9)