Answer:
(2, -2) are the coordinates of the point which divides BA into ration 2:4.
Step-by-step explanation:
The given two co-ordinates of A are (-2, 6) and B is (4, -6).
Let P be the point that divides the line BA into ratio 2:4.
to find coordinates of a point P on the line segment BA dividing it in a ratio 2:4, we can use segment formula.
[tex]x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}[/tex]
Where (x,y) is the co-ordinate of the point P which
divides the line segment joining the points [tex](x_{1}, y_{1}) and (x_{2}, y_{2})[/tex] in the ratio m:n.
Please refer to the attached image.
As per the given values :
[tex]x_{1} = 4\\x_{2} = -2\\y_{1} = -6\\y_{2} = 6\\[/tex]
Putting the given values in above formula :
x-co-ordinate of P:
[tex]x = \dfrac{4 \times 4 -2 \times 2}{4+2}\\\Rightarrow \dfrac{12}{6}\\\Rightarrow x = 2[/tex]
y-co-ordinate of P
:
[tex]y = \dfrac{4 \times -6 +2 \times 6}{4+2}\\\Rightarrow \dfrac{-24+12}{6}\\\Rightarrow \dfrac{-12}{6}\\\Rightarrow y = -2[/tex]
So, answer is P(2, -2).
