Question

1. directed line segment de has endpoints d(-4,-2) and e(1,8). point f divides de such that df:fe is 2:3. what are the coordinates of f?

a) (-3,0) b) (-2,2)
c) (-1,4) d) (2,4)

1. point p divides the directed line segment from point (-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)

1. what is the slope of a line that passes through th points (-2,-7) and (-6,-2)?

a) -4/5 b) -5/4 c) 8/9 d) 9/8

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 \(y=\frac{my_2+ny_1}{m + n}\).

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

Here, \(m = 2\), \(n=3\), \(x_1=-4\), \(x_2 = 6\).
\(x=\frac{2\times6+3\times(-4)}{2 + 3}=\frac{12-12}{5}=0\)

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

Here, \(y_1=-1\), \(y_2 = 4\).
\(y=\frac{2\times4+3\times(-1)}{2 + 3}=\frac{8 - 3}{5}=1\)

Answer:

B. \((0,1)\)