Geometry B Big Ideas 12.1
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Diagram
The example diagram to the right is not to scale for this problem. It's just an example. Your diagram needs to be drawn in an x-y coordinate plane with vertices labeled with their (x, y) coordinates. Step 1 - Draw a diagram Graph the three rosebushes as vertices of a triangle. Notice the red triangle and three vertices. |
Step 2a - Find the circumcenter
Circumcenter is covered in Lesson 5-3 page 301 of the textbook. Calculate the (x, y) coordinates for the midpoint of each side. Draw the perpendicular bisector from each midpoint. Notice the blue perpendicular bisectors in the diagram.
Step 2b
Write the equation of two of the bisectors. (Just choose two out of the three.) Calculate their intersection. The (x, y) coordinates of the intersection is the location of the circumcenter.
Step 3 - Verify the circumcenter is correct
Verify that the circumcenter is indeed equidistant to each vertex. Calculate the distance between the circumcenter and each vertex. Confirm the distances are equal.
Step 4 - Write the circle's equation
Draw the circle that inscribes the triangle. Write the equation of the circle. Use the (x, y) coordinates of the circumcenter, and the distance in Step 3 for the radius. Write the equation in standard form, simplifying if needed.
Circumcenter is covered in Lesson 5-3 page 301 of the textbook. Calculate the (x, y) coordinates for the midpoint of each side. Draw the perpendicular bisector from each midpoint. Notice the blue perpendicular bisectors in the diagram.
Step 2b
Write the equation of two of the bisectors. (Just choose two out of the three.) Calculate their intersection. The (x, y) coordinates of the intersection is the location of the circumcenter.
Step 3 - Verify the circumcenter is correct
Verify that the circumcenter is indeed equidistant to each vertex. Calculate the distance between the circumcenter and each vertex. Confirm the distances are equal.
Step 4 - Write the circle's equation
Draw the circle that inscribes the triangle. Write the equation of the circle. Use the (x, y) coordinates of the circumcenter, and the distance in Step 3 for the radius. Write the equation in standard form, simplifying if needed.