For the triangle shown below, find the circumcenter and orthocenter

Circumcenter =    Orthocenter = (-4, -6)

Step-by-step explanation for Circumcenter:

Step 1: Find the midpoint of a line: I chose (-4, 3) and (-4, -6)

Step 2: Find the perpendicular line that passes through that point:

Since it is a vertical line, the perpendicular line is

Step 3: repeat Steps 1 and 2 for another line: chose (-4, -6) and (6, -6)

Since it is a horizontal line, the perpendicular line is: x = 1

Step 4: Find the intersection of the two lines

Their point of intersection is:

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Step-by-step explanation for Orthocenter:

Step 1: Find the perpendicular slope of a line: I chose (-4, 3) and (-4, -6)

Slope is undefined. Perpendicular slope is 0.

Step 2: Use the Point-Slope formula to find the equation of the line that passes through the vertex that is opposite of the line from Step 1 and has the perpendicular slope (found in Step 1).  

Vertex (6, -6) and m⊥ = 0  ⇒  y + 6 = 0(x - 6)  ⇒  y = -6

Step 3: repeat Steps 1 and 2 for another line: chose (-4, -6) and (6, -6)

Slope is 0. Perpendicular slope is undefined (x = __ )

Vertex (-4, 3) and m⊥ = undefined  ⇒  x = -4

Step 4: Find the intersection of the two lines

Their point of intersection is: (-4, -6)

d. is the correct answer

step-by-step explanation:

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step-by-step explanation: