Answer:
R = (- 3.5, - 7 )
Step-by-step explanation:
Using the Section formula
[tex]x_{R}[/tex] = [tex]\frac{3(4)+5(-8)}{3+5}[/tex] = [tex]\frac{12-40}{8}[/tex] = [tex]\frac{-28}{8}[/tex] = - 3.5
[tex]y_{R}[/tex] = [tex]\frac{3(-2)+5(-10)}{3+5}[/tex] = [tex]\frac{-6-50}{8}[/tex] = [tex]\frac{-56}{8}[/tex] = - 7
Thus coordinates of R = (- 3.5, - 7 )
Answer: (-0.8, -5.2)
Step-by-step explanation:
The coordinates of point P(x,y) divides a line segment with endpoints A(a,b) and B(c,d) in ration m:n is given by :-
[tex]x=\dfrac{mc+na}{m+n}\ ;\ n=\dfrac{md+nb}{m+n}[/tex]
Given : Point R lies on the directed line segment from L (-8,-10) to M (4,-2) and partitions the segment in the ratio 3 to 5.
i.e. [tex]\dfrac{m}{m+n}=\dfrac{3}{3+2}[/tex]
i.e. m:n = 3:2
The coordinates of R divide directed line segment from L (-8,-10) to M (4,-2) in ratio 3:2 will be :-
[tex]x=\dfrac{3(4)+2(-8)}{3+2}\ ;\ y=\dfrac{3(-2)+2(-10)}{3+2}\\\\ x=\dfrac{12-16}{5}\ ;\ y=\dfrac{-6-20}{5}\\\\ x=-0.8\ ;\ y=-5.2[/tex]
The coordinates of R= (-0.8, -5.2)
