Prove that when the three medians of the triangle are drawn, they meet at a single point A(-5,1) B(1,7) C(1,-5). What is the point of the centroid? (1 point) Responses (−3,1) left parenthesis negative 3 comma 1 right parenthesis (−13,13) left parenthesis negative Start Fraction 1 over 3 End Fraction comma Start Fraction 1 over 3 End Fraction right parenthesis (−12,12) left parenthesis negative Start Fraction 1 over 2 End Fraction comma Start Fraction 1 over 2 End Fraction right parenthesis (−1,1)
To find the centroid of a triangle, we can use the formula:
Centroid = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3
Given the coordinates of point A(-5,1), B(1,7), and C(1,-5), we can calculate the centroid as follows:
Centroid = (-5 + 1 + 1)/3, (1 + 7 - 5)/3
= (-5 + 2)/3, (1 + 2)/3
= -3/3, 3/3
= -1, 1
Therefore, the point of the centroid is (-1, 1).