Question

Find the ratio in which line segment joining (2,3)and (4,1) is divided by the line joing (1,2) and (4,3)

Answer 1

A(2,3)
B(4,1)
C(1,2)
D(4,3)

Slope of line AB, m= y2-y1 / x2-x1 = (3-1) / (2-4)
= 2/-2 = -1

Equation:
You can take any one point for equation, I am taking B(4,1) here

(y-y1) = m (x-x1)
(y-1) = (-1) (x-4)
y-1 = 4-x
x+y = 5. (1)

Slope of line CD, m = y2-y1 / x2-x1 = (3-2) / (4-1)
= 1/3

Equation:
You can take any one point for equation, I am taking C(1,2) here

(y-y1) = m(x-x1)
(y-2) = (1/3) (x-1)
3y-6 = x-1
x-3y = -5. (2)

Solving equation (1) and (2)
y = 5/2
x = 5/2

G(5/2,5/2)

•_______k_______•_______1________•
A(2,3). G(5/2,5/2). B(4,1)

Let the ratio be k:1

k(4) + 1(2) / k+1 = 5/2
8k + 4 = 5k + 5
3k = 1
k = 1/3

k:1 = 1:3

Hope this helps... plsss make it the brainliest