Point A (4, 2) divides segment BC in ratio 2:5, where B = (2, 6) and C = (8, y).
When point A divides BC in ratio 2:5, it means BA : AC = 2 : 5.
When a point A(x, y) divides the line segment joining B(x₁, y₁) and C(x₂, y₂) in ratio m:n:
x=m+nm×x2+n×x1
y=m+nm×y2+n×y1
Given values:
A = (4, 2)
B = (2, 6), so x1=2,y1=6
C = (8, y), so x2=8,y2=y
Ratio m:n = 2:5
Using the y-coordinate formula:
2=2+52×y+5×6
2=72y+30
14=2y+30
14−30=2y
−16=2y
y=−8
Therefore, the value of y is −8.
Answer: Option 4