The st. lines `3x + 4y =5 and 4x-3y = 15` interrect at a point `A(3,-1)`. On these linepoints B and C are chosen so that `AB = AC`. Find the possible eqns of the line BC pathrough the point `(1, 2)`

Options

A. `-7,1//2`
B. 7,1/7
C. 7,-1/2
D. 3,-1/3

Answer

A

Explanation

The given equations are 3x +4y -5=0
and ` 4x -3y -15=0`
since these lines aer perpendicular to each other, so ` angle(QPR)` is right angle, Also we have PQ = PR.
Therefore , `DeltaPQR` is a right angle isoscles triangle.
` angle(PQR) = angle(PRQ) = 45^(@)`
Slope of PQ = `-3/4 and "slope of PR " = 4/3`
Let Slope of QR =m
` tan 45^(@) = |(4/3-m)/(1+4/3 m)|`
` m =1/7, -7`