The required coordinates of point B will be (2/9, -14/9).
Point A is at ( -3,4) and Point C is at ( 2,-6 )
Given that point B on line, AC suck as the ratio of AB to AC is 4:5
The coordinates of point B will be,
{[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}
Breaking it down, the x coordinate is (mx2+nx1)/(m+n) and the y coordinate is (my2+ny1)/(m+n)
As per the question, m = 4 and n = 5
The coordinates of point B :
⇒ {[(4×-3+5×2)/(4+5)],[(4×4+5×-6)/(4+5)]}
⇒ {[(-12+10)/(9)],[(16-30)/(9)]}
⇒ (2/9, -14/9)
Thus, the required coordinates of point B will be (2/9, -14/9).
Learn more about the distance between two points here:
brainly.com/question/15958176
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