Question

find the ratio in which y axis divides the line egment joining the points -4, 6 and 10, 12 also find the coordinates of the division

Answer 1

$let \: ratio \: be \: \: k: 1 \\ coordinates \: of \: division = (0.y) \\ 0 = \frac{ - 4 \times 1 + 10 \times k}{k + 1} \\ - 4 + 10k = 0 \\ k = \frac{4}{10} = \frac{2}{5} \\ ratio \: = 2: 5 \\ y = \frac{6 \times 5 + 12 \times 2}{2 + 5} = \frac{30 + 24}{7} = \frac{54}{7} \\ coordinates \: = (0 \: \: \: \: \frac{54}{7} )$