Question

point v lies on $overline{tu}$, where t is located at (-6, -4) and u is located at (10, 4). the ratio of tv to vu is 5:3. what are the coordinates of v? write your answers as integers or decimals.

Explanation:

Step1: Recall the section - formula

If a point \(V(x,y)\) divides the line - segment joining \(T(x_1,y_1)\) and \(U(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1=-6,y_1=-4,x_2 = 10,y_2 = 4,m = 5,n = 3\).

Step2: Calculate the x - coordinate of \(V\)

\[

$$\begin{align*} x&=\frac{5\times10+3\times(-6)}{5 + 3}\\ &=\frac{50-18}{8}\\ &=\frac{32}{8}\\ & = 4 \end{align*}$$

\]

Step3: Calculate the y - coordinate of \(V\)

\[

$$\begin{align*} y&=\frac{5\times4+3\times(-4)}{5 + 3}\\ &=\frac{20 - 12}{8}\\ &=\frac{8}{8}\\ &=1 \end{align*}$$

\]

Answer:

\((4,1)\)