Question

1. point p divides the directed line segment from point a (-4, -1) to point b(6,4) in the ratio 2:3. the coordinates of point p are a) (-1,1) b) (0,1) c) (1,0) d) (2,2)

Explanation:

Step1: Use the section formula

The section formula for 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 \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1=-4,y_1 = - 1,x_2=6,y_2 = 4,m = 2,n = 3\).

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

Substitute the values into the \(x\) - coordinate formula:

$$
LATEXBLOCK0
$$

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

Substitute the values into the \(y\) - coordinate formula:

$$
LATEXBLOCK1
$$

Answer:

B. \((0,1)\)