Respuesta :
The coordinates of the point P which divides the line segment AB made by the points A(-7,2) and B(9,-6) is (x,y) = (5,-4)
What is the coordinate of the point which divides a line segment in a specified ratio?
Suppose that there is a line segment [tex]\overline{AB}[/tex]such that a point P(x,y) lying on that line segment [tex]\overline{AB}[/tex] divides the line segment [tex]\overline{AB}[/tex] in m:n, then, the coordinates of the point P is given by:
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]
where we have:
- the coordinate of A is [tex](x_1, y_1)[/tex]
- and the coordinate of B is [tex](x_2, y_2)[/tex]
We're given that:
- Coordinate of A is [tex](x_1, y_1)[/tex] = (-7,2)
- Coordinate of B is [tex](x_2, y_2)[/tex] = (9.-6)
- The point P lies on AB such that AP:BP=3:1 (so m = 3, and n = 1)
Let the coordinate of P be (x,y), then we get the values of x and y as:
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)\\\\(x,y) = \left( \dfrac{3(9) + 1(-7)}{3+1} , \dfrac{3(-6) + 1(2)}{3+1} \right)\\\\(x,y) = \left( \dfrac{20}{4} , \dfrac{-16}{4} \right) = (5,-4)[/tex]
Thus, the coordinates of the point P which divides the line segment AB made by the points A(-7,2) and B(9,-6) is (x,y) = (5,-4)
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