Question

point b partitions ac in the ratio 1:3. what are the coordinates of c? the coordinates of c are (simplify your answer. type an ordered pair.)

Explanation:

1. Assume the coordinates of \(A(x_1,y_1)\) and \(B(x_2,y_2)\):

• Although the coordinates of \(A\) and \(B\) are not explicitly given in text, from the graph, assume \(A(- 4,4)\) and \(C(6,-12)\).
• The section - formula for a point \(B(x,y)\) that divides the line - segment joining \(A(x_1,y_1)\) and \(C(x_2,y_2)\) in the ratio \(m:n\) is given by \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 1\) and \(n = 3\).

1. Calculate the \(x\) - coordinate of \(B\):

• \(x=\frac{1\times6+3\times(-4)}{1 + 3}=\frac{6-12}{4}=\frac{-6}{4}=-\frac{3}{2}\).

1. Calculate the \(y\) - coordinate of \(B\):

• \(y=\frac{1\times(-12)+3\times4}{1 + 3}=\frac{-12 + 12}{4}=0\).

Answer:

\((-\frac{3}{2},0)\)