Question

A(13,5) B(4,-3) and A-P-B find the ratio on which point P(9,2) divides segment AB​

Answer 1

Answer:

3 : 5

Step-by-step explanation:

Correct Question :-

A (12,5) ,B (4,-3) and A-P-B . Find the ratio in which point P (9,2) divides segment AB.

Given ,

A = (12 , 5)

B = (4 , - 3)

P = (9 , 2)

To Find :-

The ratio that 'P' divides the line segment AB.

Formula Required :-

Section(Internal Division) Formula :-

$(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Solution :-

Let the ratio be 'm : n'

A = (12 , 5)

Let ,

x_1 = 12 , y_1 = 5

B = (4 , - 3)

Let,

x_2 = 4 , y_2 = - 3

P = (9 , 2)

Let,

x = 9 , y = 2

Substituting these values in formula :-

$(9,2)=\left(\dfrac{m(4)+n(12)}{m+n},\dfrac{m(-3)+n(5)}{m+n}\right)$

$(9,2)=\left(\dfrac{4m+12n}{m+n},\dfrac{-3m+5n}{m+n}\right)$

Equating both 'x' terms and 'y' terms :-

$9=\dfrac{4m+12n}{m+n},2=\dfrac{-3m+5n}{m+n}$

Solving for both 'x' terms :-

$9=\dfrac{4m+13n}{m+n}$

9(m + n) = 4m + 12n

9m + 9n = 4m + 12n

9m - 4m = 12n - 9n

5m = 3n

5m/n = 3

m/n = 3/5

m : n = 3 : 5

Solving 'y' terms :-

$2=\dfrac{-3m+5n}{m+n}$

2(m + n) = -3m + 5n

2m + 2n = - 3m + 5n

2m + 3m = 5n - 2n

5m = 3n

5m/n = 3

m/n = 3/5

m : n = 3 : 5

∴ Ratio = m : n = 3 : 5

Answer 2

Answer:

all steps are done properly by me i thik it's right