Question

A city planner is mapping out some new features for a triangular park. She sketches the park on grid paper. The coordinates of the vertices of the park are (1, 1), (1, 4), and (−3, 4).   The city planner wants to put a flower bed at the centroid of the park. What are the coordinates of the flower bed? (__,__)​

Answer 1

Answer:

The coordinates of the flower bed are ($-\frac{1}{3}$ , 3)

Step-by-step explanation:

To find the centroid of a triangle, use this rule centroid = ($\frac{x1+x2+x3}{3},\frac{y1+y2+y3}{3}$), where (x1, y1), (x2, y2), (x3, y3) are the vertices of the triangle

∵ The vertices of the triangle are (1, 1), (1, 4), (-3, 4)

∴ x1 = 1 and y1 = 1

∴ x2 = 1 and y2 = 4

∴ x3 = -3 and y3 = 4

→ Substitute them in the rule above

∵ Centroid = ($\frac{1+1+-3}{3},\frac{1+4+4}{3}$)

∴ Centroid = ($\frac{-1}{3},\frac{9}{3}$)

∴ Centroid = ($-\frac{1}{3}$ , 3)

∴ The coordinates of the flower bed are ($-\frac{1}{3}$ , 3)