Question

Point C(3.6, -0.4) divides AB in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are ____ . If point D divides in the ratio 4 : 5, the coordinates of point D are____ .

Answer 1

Answer:

the coordinates of  Point B are  ( 10  , -4)

the coordinates of point D are ( 10/9  , 1)

Step-by-step explanation:

Point C(3.6, -0.4) divides AB in the ratio 3 : 2.

The coordinates of A are (-6, 5),

we need to find the coordinates of point B

Let say coordinates  of point B ( x , y)

if point C divides line AB into m:n ratio

Xc =  (mBx + nAx)/(m + n)  

Yc = (mBy + nAy)/(m + n)

=> 3.6 = (3x + 2(-6))/(3 + 2)

=> 18 = 3x - 12

=> 3x = 30

=> x = 10

-0.4 = (3y + 2(5))/(3 + 2)

=> -2 = 3y + 10

=> 3y = -12

=> y = -4

the coordinates of  Point B are  ( 10  , -4)

point D  divides AB in ration 4 : 5  

A = (-6 , 5)   B =(10 , -4)

Dx = (4*10 + 5(-6))/(4 + 5) = 10/9

Dy = (4*(-4) + 5*5)/(4 + 5) = 9/9 = 1

the coordinates of point D are ( 10/9  , 1)

Answer 2

Answer:

Step-by-step explanation:

Point C(3.6, -0.4) (Given)

Coordinates of A are (-6, 5)

Ratio by point C = 3:2.

Ratio by point D = 4:5

Let the coordinates  of point B = ( x , y)

Let point C divide the line AB into ratio - m:n, thus

Xc =  (mBx + nAx)/(m + n)  

Yc = (mBy + nAy)/(m + n)

= 3.6 = (3x + 2(-6))/(3 + 2)

= 18 = 3x - 12

= 3x = 30

= x = 10

-0.4 = (3y + 2(5))/(3 + 2)

= -2 = 3y + 10

= 3y = -12

y = -4

Thus, the coordinates of  Point B are  ( 10 and -4)

Point D  divides AB in ration 4 : 5  

A = (-6 , 5)   B =(10 , -4)

Dx = (4 × 10 + 5(-6))/(4 + 5)

= 10/9

Dy = (4 × (-4) + 5×5)/(4 + 5)

= 9/9 = 1

Therefore, the coordinates of point D are ( 10/9, 1)