Respuesta :
Answer:
[tex](5.75,4.25)[/tex]
Step-by-step explanation:
We have been given that line segment AB has endpoints A(7, 4) and B(2, 5). We are asked to find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3.
To solve our given problem we will use section formula.
Section formula states, when a point P divides a line segment AB internally in ratio m:n, so the coordinates of point P are:
[tex]P(x,y)=[x=\frac{m\cdot x_2+n\cdot x_1}{m+n},y=\frac{m\cdot y_2+n\cdot y_1}{m+n}][/tex]
Let [tex](7,4)=(x_1,y_1)[/tex], [tex](2,5)=(x_2,y_2)[/tex], [tex]m=1\text{ and }n=3[/tex].
Upon substituting coordinates of our given points in section formula we will get,
[tex]P(x,y)=[x=\frac{1\cdot 2+3\cdot 7}{1+3},y=\frac{1\cdot 5+3\cdot 4}{1+3}][/tex]
[tex]P(x,y)=[x=\frac{2+21}{4},y=\frac{5+12}{4}][/tex]
[tex]P(x,y)=[x=\frac{23}{4},y=\frac{17}{4}][/tex]
[tex]P(x,y)=[x=5.75,y=4.25][/tex]
Therefore, the coordinates of point that divides the line segment AB in the ratio 1:3 are [tex](5.75,4.25)[/tex].
