Question

1. fill in the blanks using the available answer choices. find d on $overline{af}$ that is $\frac{3}{5}$ the distance from a to f. point d is located at (blank 1) blank 1 options: (0, 1) (2, 3) (4, 4) (4, 5) a(-2, -1) f(8, 9)

Explanation:

Step1: Use section - formula

The section - formula for a point \(D(x,y)\) that divides the line - segment joining \(A(x_1,y_1)\) and \(F(x_2,y_2)\) 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, \(m = 3\), \(n=2\), \(x_1=-2\), \(y_1=-1\), \(x_2 = 8\), \(y_2=9\).

Step2: Calculate the x - coordinate of point D

\[x=\frac{3\times8+2\times(-2)}{3 + 2}=\frac{24-4}{5}=\frac{20}{5}=4\]

Step3: Calculate the y - coordinate of point D

\[y=\frac{3\times9+2\times(-1)}{3 + 2}=\frac{27-2}{5}=\frac{25}{5}=5\]

Answer:

\((4,5)\)