Question

find the equation of the straight line through (-4,9) and (4,3). Find the coordinates of the point where it meets the axes. Also find the portion of the straight line intercepted between the axes.​

Answer 1

Step-by-step explanation:

Toolbox:

Section formula : The coordinates of the point which divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n is (mx2+nx1m+n,my2+ny1m+n)

Step 1:

Let the equation of the line be xa+yb=1. This line meets the coordinates axes at A(a,0) and B(0,b) respectively. The coordinates of the point which divides the line joining A(a,0) and B(0, b) in the ratio 5:3 are

[5×(0)+3(a)5+3,5×(b)+3(0)5+3]

(i.e) The coordinates are

⇒(3a8,5b8)

Step 2 :

It is given that the point (-4, 3) divides AB in the ratio 5 : 3

∴3a8=−4⇒a=−333

and 5b8=3⇒=245

Hence the equation of the line is

x−323+y245=1

(i.e) 9x−20y=−96

9x−20y+96=0

Hence the equation of the required line is 9x−20y+96=0

Answer 2

please see the attachment