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:

(3,-2), (3, 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 tree?

Answer 1

The centroid of the triangle with vertices at (3,-2), (3, 4), and (-3, 4) is calculated by averaging the x and y coordinates separately, resulting in the point (1, 2), which is where the city planner should place the flower bed.

Step-by-step explanation:

To find the centroid of the triangular park, you need to calculate the average of the x-coordinates and the y-coordinates of the vertices of the triangle. The coordinates of the vertices of the park are (3,-2), (3, 4), and (-3, 4).

The formula for finding the centroid (x, y) is given by:

x = (x1 + x2 + x3) / 3

y = (y1 + y2 + y3) / 3

For x-coordinates:

x = (3 + 3 + (-3)) / 3 = 3 / 3 = 1

For y-coordinates:

y = (-2 + 4 + 4) / 3 = 6 / 3 = 2

Therefore, the coordinates of the centroid, which is where the city planner wants to put a flower bed, are (1, 2).