Machinists often use a coordinate system to drill holes by placing the origin at the most convenient location. A bolt circle is the circle formed by completing an arc through the centers of the bolt holes in a piece of metal. Find the coordinates of the centers of points A, D, and G for the equally spaced $\frac { 1 } { 3 }$ -in. holes on a bolt circle of radius 7.00 in., as shown in the illustration. Round your answer to the nearest tenth.
A) A = (-4.9, 0.0) D = (7.0, 4.9) G = (0.0, -7.0)
B) A = (7.0, 0.0) D = (-4.9, -7.0) G = (0.0, 0.0)
C) A = (7.0, 0.0) D = (-4.9, 4.9) G = (0.0, -7.0)
D) A = (7.0, -7.0) D = (-4.9, 4.9) G = (0.0, 0.0)

Question

Machinists often use a coordinate system to drill holes by placing the origin at the most convenient location. A bolt circle is the circle formed by completing an arc through the centers of the bolt holes in a piece of metal. Find the coordinates of the centers of points A, D, and G for the equally spaced $\frac { 1 } { 3 }$ -in. holes on a bolt circle of radius 7.00 in., as shown in the illustration. Round your answer to the nearest tenth. 
A) A = (-4.9, 0.0) D = (7.0, 4.9) G = (0.0, -7.0) 
B) A = (7.0, 0.0) D = (-4.9, -7.0) G = (0.0, 0.0) 
C) A = (7.0, 0.0) D = (-4.9, 4.9) G = (0.0, -7.0) 
D) A = (7.0, -7.0) D = (-4.9, 4.9) G = (0.0, 0.0)

Quizplus · Accepted Answer

We can use the unit circle to find the coordinates of the centers of the points on the bolt circle. Let's assume that the center of the bolt circle is at the origin (0,0). Then, we can find the coordinates of the points A, D, and G by using angles that are multiples of 120 degrees (since the holes are equally spaced).

Point A:
Angle = 120 degrees
x-coordinate = r*cos(angle) = 7*cos(120) = -3.5
y-coordinate = r*sin(angle) = 7*sin(120) = 6.1
Therefore, the coordinates of point A are (-3.5, 6.1).

Point D:
Angle = 240 degrees
x-coordinate = r*cos(angle) = 7*cos(240) = -4.9
y-coordinate = r*sin(angle) = 7*sin(240) = -4.9
Therefore, the coordinates of point D are (-4.9, -4.9).

Point G:
Angle = 0 degrees
x-coordinate = r*cos(angle) = 7*cos(0) = 7.0
y-coordinate = r*sin(angle) = 7*sin(0) = 0.0
Therefore, the coordinates of point G are (7.0, 0.0).

The only choice that matches these coordinates is C.

Machinists Often Use a Coordinate System to Drill Holes by Placing