Let D be a region bounded by a simple closed path C in the xy. Then the coordinates of the centroid where A is the area of D. Find the centroid of the triangle with vertices (0, 0), ( , 0) and (0, ).

Question

Let D be a region bounded by a simple closed path C in the xy. Then the coordinates of the centroid  where A is the area of D. Find the centroid of the triangle with vertices (0, 0), (  , 0) and (0,  ).

Quizplus · Accepted Answer

The centroid of any region with a simple closed path C is given by:
(11eaa3e5_54c0_c868_9f8f_db017abf25c5_TB5971_11)
where A is the area of the region and (x,y) represents the coordinates of any point within the region.

For the triangle with vertices (0, 0), (11eaa3e5_54c0_ef79_9f8f_075812167716_TB5971_11, 0) and (0, 11eaa3e5_54c0_ef7a_9f8f_d1f46e21c0b9_TB5971_11), we can use the formula:

Centroid_x = (x1 + x2 + x3)/3
Centroid_y = (y1 + y2 + y3)/3

where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the vertices.

Plugging in the values, we get:
Centroid_x = (0 + 11eaa3e5_54c0_ef79_9f8f_075812167716_TB5971_11 + 0)/3 = 11eaa3e5_54c0_ef7e_9f8f_b52619838739_TB5971_11
Centroid_y = (0 + 0 + 11eaa3e5_54c0_ef7a_9f8f_d1f46e21c0b9_TB5971_11)/3 = 11eaa3e5_54c0_ef7f_9f8f_ed782f077129_TB5971_11

Therefore, the centroid of the triangle is (11eaa3e5_54c0_ef7e_9f8f_b52619838739_TB5971_11, 11eaa3e5_54c0_ef7f_9f8f_ed782f077129_TB5971_11), which is closest to choice C: 11eaa3e5_54c0_ef7d_9f8f_677bc5711d64_TB5971_11.

Let D Be a Region Bounded by a Simple Closed