Question

1. answer the following questions to the best of your ability. - no work required to be shown.

a) which of the following diagrams best represent the construction of a centroid?
(images of choice a, choice b, choice c, choice d are shown)
options: choice d, choice c, choice a, choice b
b) which of the following constructs the point of concurrency in (a)?
options: perpendicular bisectors, altitudes, medians, angle bisectors
c) which of the following is a special property of the point of concurrency in (a)?
options: this point of concurrency is the location in the triangle that can be perfectly balanced on a pencil tip without falling.
this point of concurrency is the location in the triangle that is equidistant from all of the sides of the triangle.
this point of concurrency is the location in the triangle that will be located on the vertex of the right angle of a right triangle.
this point of concurrency is the center of the circle that contains all three vertices of the triangle.

1. what are the exact coordinates for the...

(another triangle problem with parts a, b, c and a triangle diagram)

1. if a triangle is defined by vertices a...

Explanation:

Part (a)

The circumcenter of a triangle is the intersection of the perpendicular bisectors of the triangle's sides. To construct the circumcenter, we draw the perpendicular bisectors of at least two sides of the triangle. Looking at the choices, Choice A shows the construction of perpendicular bisectors (the arcs and lines suggest bisecting the sides at right angles), which is the correct way to find the circumcenter.

The circumcenter is the point of concurrency of the perpendicular bisectors of the sides of a triangle. Altitudes are for the orthocenter, medians for the centroid, and angle bisectors for the incenter. So the correct construct for the circumcenter (point of concurrency in part (a)) is perpendicular bisectors.

• The first option describes the centroid (balance point).
• The second option describes a point equidistant from sides, which is the incenter.
• The third option is incorrect as the circumcenter isn't related to the right - angle vertex in that way.
• The fourth option: The circumcenter is the center of the circumscribed circle (circumcircle) that passes through all three vertices of the triangle. This matches the property of the circumcenter.

Answer:

Choice A

Part (b)