Point A (4, 2) divides segment BC in the ratio 2 : 5. Coordinates of B and C are (2, 6), (9, y) respectively. Find the value of y.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → -8
By the section formula, the point that divides the segment from \(B(x_1,y_1)\) to \(C(x_2,y_2)\) in the ratio \(m:n\) has \(y=\frac{my_2+ny_1}{m+n}\): each end is weighted by the part of the ratio next to the other end.
The equation (the formula set equal to A’s y-coordinate):
\(m:n=2:5\), \(B(2,6)\), \(C(9,y)\), and the point A has \(y=2\)
Putting these into the formula: \(\displaystyle \frac{2\times y+5\times6}{2+5}=2\)
Finding \(y\):
\(2y+30=14\)
\(2y=-16\), so \(y=-8\)