Question

Calculate the ratio in which the line joining A(5, 6) and B(-3, 4) is divided
x = 2. Also, find the point of intersection.​

Answer 1

Step-by-step explanation:

By the formula,

x = (x1 m + x2 n) ÷ ( m + n) ( where m and n are the ratio)

2= ( 5 × m + (-3) n) ÷ ( m + n)

2m+ 2n = 5m - 3n

3n + 2n = 5m - 2m

7n = 3m

m/n = 7/3

hence, the ratio is 7/3

y = (6m + 4n) ÷ ( m +n)

ym + yn = 6m + 4n

n ( y - 4) = m ( 6-y)

m/n = ( y- 4)/( 6- y)

from above

(y-4) / (6-y) = 7/3

3y - 12 = 42 - 7y

10y = 42+12

10y = 54

y = 5.4

therefore, the point of intersection are ( 2, 5.4 )