Question

hi there

please answer

maths legend and brainly genius

Answer 1

Answer:

72x-96y=7

Step-by-step explanation:

Given, equation,

4x + 3x + 1 = 0

Gradient  of  this  line = -coff. of x/coff. of y

                      m₁ = -4/3

Re-Write  in Standard form of  equation, x/a + y/b = 1 Where  a = Section cut on x-axis, b= section cut  on y axis.

4x + 3y = -1

$\frac{x}{-1/4}+\frac{y}{-1/3}=1\\\;$

Hence, We can say that,

a = -1\4

b = - 1/3

Also it  cuts  the  axis in negative  direction of  axis  both x and y

If  the line cuts  the  axis  at P(at x-axis) and  Q(at y-axis)  the,

Co-ordinates of P = (-1/4,0)

Co-ordinates of Q = (0, -1/3)

Find The  Mid-Point of  PQ:-

Using  Section Formula,

if  Mid-point  of  PQ  is  R, Then,

Co-ordinates  of  R = $(\frac{-1/4+0}{2},\frac{0+(-1/3)}{2})$

Co-ordinates  of  R = (-1/8, -1/6)

Gradient  of  The  line  Perpendicular on PQ, (m₂) = -1/m₁

m₂ = -1/(-4/3)

m₂ = 3/4

Now, Equation of  line Passing through Points (-1/8, -1/6) having gradient 3/4 ,

y-(-1/6)=3/4(x-(-1/8))

$y+\frac{1}{6}=\frac{3}{4}(x+\frac{1}{8})\\\;\\\frac{6y+1}{6}=\frac{3}{4}(\frac{8x+1}{8})\\\;\\\frac{6y+1}{3}=\frac{3}{16}(8x+1)\\\;\\16(6y+1)=9(8x+1)\\\;\\96y+16=72x+9\\\;\\72x-96y=7\\\;\\\textbf{This is the required equation}$

Note:-

$\text{Equation of Line passing through point}\;(x_1,y_1)\;\text{Having gradient m}\\y-y_1=m(x-x_1)$