Question

Find the equation of the straight line which divide the join of the points (2,3) and (-5,8) in the ratio 3:4 and is also perpendicular to it.

Answer 1

OK this is the answer I think

Answer 2

Answer:

Equation of the line is $y=\frac{7x}{5}+\frac{229}{35}$

Step-by-step explanation:

If a line segment joining two points (x, y) and (x', y') is divided by a perpendicular line at point (a, b) in the ratio of m : n.

Then $(a, b) = [\frac{mx'+nx}{m+n}, \frac{my'+ny}{m+n}]$

If these points are (2, 3) and (-5, 8) and (a, b) divides the segment joining these points in 3 : 4 then,

$(a, b)=[\frac{3\times (-5)+4(2)}{3+4},\frac{8(3)+4\times 3}{3+4}]$

        = $[\frac{-7}{7}, \frac{36}{7}]$

        = $[(-1), \frac{36}{7}]$

Slope of a line passing through (2, 3) and (-5, 8) will be

m = $\frac{8-3}{-5-2}$

m = $-\frac{5}{7}$

By the property of slopes of perpendicular lines,

$m_{1}\times m_{2}=-1$

$m_{1}\times (-\frac{5}{7})=-1$

$m_{1}=\frac{7}{5}$

Therefore, equation of a line passing through $[(-1), \frac{36}{7}]$ and slope $\frac{7}{5}$

y - b = m(x - a)

$y-\frac{36}{7}=\frac{7}{5}(x+1)$

$y=\frac{7x}{5}+\frac{7}{5}+\frac{36}{7}$

y = $\frac{7x}{5}+\frac{229}{35}$

Therefore, equation of the line is $y=\frac{7x}{5}+\frac{229}{35}$

Learn more about the slopes and equation of the line from https://brainly.in/question/2907207