what are the coordinates of the centroid of $\\triangle jkl$? simplify any fractions.
what are the coordinates of the centroid of $\\triangle jkl$? simplify any fractions.
Answer
Explanation:
Step1: Identify coordinates of vertices
From the graph, we find the coordinates of ( J ), ( K ), and ( L ):
- ( J(-2, -1) )
- ( K(2, 7) )
- ( L(-9, 6) )
Step2: Use centroid formula
The centroid ( (x, y) ) of a triangle with vertices ( (x_1, y_1) ), ( (x_2, y_2) ), ( (x_3, y_3) ) is given by: [ x = \frac{x_1 + x_2 + x_3}{3}, \quad y = \frac{y_1 + y_2 + y_3}{3} ]
Step3: Calculate x-coordinate
Substitute ( x_1 = -2 ), ( x_2 = 2 ), ( x_3 = -9 ): [ x = \frac{-2 + 2 + (-9)}{3} = \frac{-9}{3} = -3 ]
Step4: Calculate y-coordinate
Substitute ( y_1 = -1 ), ( y_2 = 7 ), ( y_3 = 6 ): [ y = \frac{-1 + 7 + 6}{3} = \frac{12}{3} = 4 ]
Answer:
((-3, 4))