Question

Given, A(– 5, – 2) and B(6, 8). Find the equation of the line AB. Find the ratio on y-axis where P divides AB. Find also the distance AB.

Answer 1

Solution:

1) Equation of line AB:

equation of a line passing through two points (x1,y1) and (x2,y2)

$y - y_{1} = \bigg(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\bigg) (x - x_{1}) \\ \\ y + 2 = \bigg(\frac{8 + 2}{6 + 5}\bigg)( x + 5) \\ \\ y + 2 = \frac{10}{11} (x + 5) \\ \\ 11y + 22 = 10x + 50 \\ \\ - 10x + 11y = 50 - 22 \\ \\ 10x - 11y = - 28$

2) Ratio in which P(0,y) divides the line segment:

let the point P divides the line segment in k:1

So by section formula

$0 = \frac{ - 5(k) +6 }{k + 1} \\ \\ - 5k = - 6 \\ \\ k = \frac{6}{5}$
Hence point P divides the line segment in 6:5 Ratio.

3) Distance of AB:

by distance formula
$\sqrt{ {( - 5 - 6)}^{2} + {( - 2 - 8)}^{2} } \\ \\ = \sqrt{121 + 100} \\ \\ = \sqrt{221} \\ \\ = 14.86 \: units$

Hope it helps you.