Answer:
The coordinates of [tex]P = (x,y) = (-\frac{3}{2} , -\frac{3}{2})[/tex]
Step-by-step explanation:
Coordinates of A= (1,6) and B = (-2,-3)
AP:PB = 5:1
Let the coordinates of P =(x,y)
Now, by SECTION FORMULA:
If m1: m2 is the ratio between two segments, then the coordinate of point is given as [tex](x,y) = (\frac{m1x_2+ m2x_1}{m1+m2} , \frac{m1y_2+ m2y_1}{m1+m2} )[/tex]
Similarly here, (x1, y1) = (1,6) , (x2, y2) = (-2,-3) and m1: m2 = 5: 1
Putting all values in equation, we get:
[tex](x,y) = (\frac{5(-2)+ 1(1)}{5+1} , \frac{5(-3)+1(6)}{5+1} )[/tex]
or, [tex](x,y) = (\frac{-10 + 1}{6} , \frac{-15 + 6}{6} ) = (\frac{-9}{6} , \frac{-9}{6} )[/tex]
Hence, the coordinates of [tex]P = (x,y) = (-\frac{3}{2} , -\frac{3}{2})[/tex]
