Question

what are the coordinates of the point on the directed line segment from (-7, -10) to (1, -6) that partitions the segment into a ratio of 3 to 1?

Explanation:

Step1: Recall the section - formula

The formula to find the coordinates of a point \(P(x,y)\) 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, \(x_1=-7,y_1=-10,x_2 = 1,y_2=-6,m = 3,n = 1\).

Step2: Calculate the x - coordinate

Substitute the values into the x - coordinate formula:

$$
LATEXBLOCK0
$$

Step3: Calculate the y - coordinate

Substitute the values into the y - coordinate formula:

$$
LATEXBLOCK1
$$

Answer:

\((-1,-7)\)