Question

1. Given points A(3, -5) and B(19, -1), find the coordinates of point C that sit 3/8 of the way along line AB, closer to A than to B.

2. Given points A(3, -5) and B(19, -1), find the coordinates of point C such that CB/AC = 1/7

Answer 1

1. C(x, y) = (7.3, –3.9)

2. C(x, y) = (17, –1.5)

Solution:

Question 1:

Let the points are A(3, –5) and B(19, –1).

C is the point that on the segment AB in the fraction
`(3)/(8)`.

Point divides segment in the ratio formula:

`$C(x, y)=\left((mx_2+nx_1)/(m+n) , (my_2+ny_1)/(m+n)\right)`

Here,
`x_1=3, y_1=-5, x_2=19, y_2=-1` and m = 3, n = 8

`$C(x, y)=\left((3*19+8*3)/(3+8) , (3*(-1)+8*(-5))/(3+8)\right)`

`$=\left((57+24)/(11) , (-3-40)/(11)\right)`

`$=\left((81)/(11) , (-43)/(11)\right)`

C(x, y) = (7.3, –3.9)

Question 2:

Let the points are A(3, –5) and B(19, –1).

C is the point that on the segment AB in the fraction
`(3)/(8)`.

Point divides segment in the ratio formula:

`$C(x, y)=\left((mx_2+nx_1)/(m+n) , (my_2+ny_1)/(m+n)\right)`

Here,
`x_1=3, y_1=-5, x_2=19, y_2=-1` and m = 7, n = 1

`$C(x, y)=\left((7*19+1*3)/(7+1) , (7*(-1)+1*(-5))/(7+1)\right)`

`$=\left((133+3)/(8) , (-7-5)/(8)\right)`

`$=\left((136)/(8) , (-12)/(8)\right)`

C(x, y) = (17, –1.5)