Question

given the points m(-3, -4) and t(5, 0). find the coordinates of the point q on directed line segment mt that partitions mt in the ratio 2:3.

Explanation:

Step1: Recall the section - formula

The formula to find the coordinates of a point \(Q(x,y)\) that divides the line - segment joining \(M(x_1,y_1)\) and \(T(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1=-3,y_1=-4,x_2 = 5,y_2 = 0,m = 2,n = 3\).

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

$$
LATEXBLOCK0
$$

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

$$
LATEXBLOCK1
$$

Answer:

\((0.2,-2.4)\)