Question

find the ratio in which y-axis divides a line segment joining the points A(5,-6) and B(-1,-4). Also find the coordination of point of division.​

Answer 1

Step-by-step explanation:

Let the point P(0, b) be on y -axis which divides the segment AB in the ratio m : n

$A(5,-6)=(x_1, y_1)\\B(-1,-4)=(x_2, y_2)\\P(0, b)=(x, y)$

Now by section formula for internal division, we have:

$\: \: \: \: \: \: \: x = \frac{mx_2 + nx_1}{m + n} \\ \implies \: 0 = \frac{m( - 1) + n \times 5}{m + n} \\ \implies \: 0 = \frac{ - m + 5n}{m + n} \\ \implies \: 0 \times (m + n)= - m + 5n \\ \implies \: 0 = - m + 5n \\ \implies \: m = 5n \\ \implies \: \frac{m}{n} = \frac{5}{1} \\ \implies \: \huge \fbox{ m : n = 5 : 1 }\\ now \: \\ \\ \: \: \: \: \: \: \: y = \frac{my_2 + ny_1}{m + n} \\ \implies \: b = \frac{5( - 4) + 1 ( - 6)}{5 + 1} \\ \implies \: b = \frac{ - 20 - 6}{6} \\ \implies \: b = \frac{ - 26}{6} \\ \implies \: b = \frac{ - 13}{3} \\ thus \: P(0, b) = P(0, \frac{ - 13}{3}) \: is \: the \\ coordinate \: of \: point \: of \: division.$