Respuesta :
Answer:
The required sets of coordinates are (-4,28) and (-4,20).
Step-by-step explanation:
Given information: A (-4, 16) and B (-4, 32).
Section formula:
If end point of a line segment are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] and a point divides that line segment in m:n, then the coordinates of that point are
[tex](\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]
If a point divides AB in 3:1, then coordinates of that point are
[tex](\frac{(3)(-4)+(1)(-4)}{3+1},\frac{(3)(32)+(1)(16)}{3+1})[/tex]
[tex](\frac{-12-4}{4},\frac{96+16}{4})[/tex]
[tex](\frac{-16}{4},\frac{112}{4})[/tex]
[tex](-4,28)[/tex]
If a point divides AB in 1:3, then coordinates of that point are
[tex](\frac{(1)(-4)+(3)(-4)}{1+3},\frac{(1)(32)+(3)(16)}{1+3})[/tex]
[tex](\frac{-4-12}{4},\frac{32+48}{4})[/tex]
[tex](\frac{-16}{4},\frac{80}{4})[/tex]
[tex](-4,20)[/tex]
Therefore the required sets of coordinates are (-4,28) and (-4,20).
