Question

determine the coordinates of point t that divides \\( \overline { a b } \\) into two segments in the ratio 1:3. write your responses as decimal values (if necessary) to the hundredths place
(1 point)
t is located at \\( \square \square \\)

Explanation:

Step1: Find the coordinates of points A and B

From the graph, \(A=(0,0)\) and \(B=(5,3.5)\).

Step2: Use the section formula

The section formula for a point \(T(x,y)\) that divides the line - segment joining \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here \(m = 1\), \(n = 3\), \(x_1=0\), \(y_1 = 0\), \(x_2=5\), \(y_2=3.5\).
For \(x\) - coordinate:
\(x=\frac{1\times5+3\times0}{1 + 3}=\frac{5}{4}=1.25\)
For \(y\) - coordinate:
\(y=\frac{1\times3.5+3\times0}{1 + 3}=\frac{3.5}{4}=0.875\approx0.88\)

Answer:

\((1.25,0.88)\)