Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are .

A (5,-4)

B (5,-2)

C (10,-4)

D (10,-2)

If point D divides in the ratio 4 : 5, the coordinates of point D are .

A (62/9,-4)

B (58/9,-4)

AceOfMath May 10, 2019

#1**+2 **

Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are .

I'm assuming that C divides * AB* in the ratio of 3 : 2

We have 5 equalline segments on AB and C are 3 of these

We can find the x coordinate of B, thusly :

[ -6 + (3/5) ( x coordinate of B - - 6 ] = 3.6 add 6 to both sides

(3/5)(x coordinate of B + 6 ) = 9.6 multiply both side by (5/3)

x coordinate of B + 6 = 16 subtract 6 form both sides

x coordinate of B = 10

Similarly, we can find the y coordinate of B thusly.....

[ 5 + (3/5)( y coordinate of B - 5) = -0.4 subtract 5 from both sides

(3/5) (y coordinate of B - 5) = -5.4 multiply both sides by 5/3

y coordinate of B - 5 = -9 add 5 to both sides

y coordinate of B = -4

So....B = ( 10 , - 4) ⇒ "C"

See the graph, here : https://www.desmos.com/calculator/hfo8kkx0lp

CPhill May 10, 2019