Question

use the image to answer the question

image long description

determine the coordinates of point c that divides (overline{ab}) into two segments in the ratio 1:4. write your responses as decimal values (if necessary) to the tenths place.

(1 point)

c is located at (□□)

Explanation:

Step1: Find the coordinates of points A and B

From the graph, \(A=(0,0)\) and \(B = (-8,2)\)

Step2: Use the section formula

The section formula for a point \(C(x,y)\) that divides the line - segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) 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 \(m = 1\), \(n=4\), \(x_1 = 0\), \(y_1=0\), \(x_2=-8\), \(y_2 = 2\)

Calculate \(x\) - coordinate

\(x=\frac{1\times(-8)+4\times0}{1 + 4}=\frac{-8+0}{5}=-1.6\)

Calculate \(y\) - coordinate

\(y=\frac{1\times2+4\times0}{1 + 4}=\frac{2+0}{5}=0.4\)

Answer:

\((-1.6,0.4)\)