Find the coordinates of the point C ,if the point B (1/2,6) divides the line segment joining the points A(3,5) and C in the ratio 1:3

Question

Solve stepwise and easy way 

Grade -9 concept 

Coordinate geometry

Answer 1

draw the line segment

A____B____________C

A=(3,5), B=(1/2,6), C=(x,y)

find the slope, the rise over the run

(6-5)/([1/2]-3)=1/-2.5=-2/5

B is 3/4 of the way from C to A

add 3/4 of the run to x and add 3/4 of the rise to y; this will give you the coordinates of B, which we know

(3/4)*(-2)=-3/2; add this to y to get (-3/2 + y)

(3/4)*(5)=15/4; add this to x to get (15/4 + x)

these are the coordinates of point B

but we already know the coordinates of point B: (1/2, 6)

so set the x's equal to each other and set the y's equal to each other

15/4 +x=1/2

x=1/2-15/4

x=-13/4

x=-3.25

-3/2 +y=6

y=7.5

the coordinates of C are (-3.25,7.5)  (answer)

check: find the slope using these coordinates (it should be -2/5)

use point A=(3,5)

(5-7.5)/(3-[-3.25])

-2.5/6.25

-250/625

simplify, divide both terms by 25

-10/25

divide both terms by 5

-2/5

check !!!