Question

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. What are the coordinates of point R

Answer 1

Answer:

R = (- 3.5, - 7 )

Step-by-step explanation:

Using the Section formula

$x_{R}$ = $\frac{3(4)+5(-8)}{3+5}$ = $\frac{12-40}{8}$ = $\frac{-28}{8}$ = - 3.5

$y_{R}$ = $\frac{3(-2)+5(-10)}{3+5}$ = $\frac{-6-50}{8}$ = $\frac{-56}{8}$ = - 7

Thus coordinates of R = (- 3.5, - 7 )

Answer 2

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 :-

$x=\dfrac{mc+na}{m+n}\ ;\ n=\dfrac{md+nb}{m+n}$

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. $\dfrac{m}{m+n}=\dfrac{3}{3+2}$

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 :-

$x=\dfrac{3(4)+2(-8)}{3+2}\ ;\ y=\dfrac{3(-2)+2(-10)}{3+2}\\\\ x=\dfrac{12-16}{5}\ ;\ y=\dfrac{-6-20}{5}\\\\ x=-0.8\ ;\ y=-5.2$

The coordinates of R= (-0.8, -5.2)