The triangle formed by the lines $2x+3y-5=0,x-y+4=0\text{ and }6x-4y+1=0\text{ is}$

detailed solution

Correct option is A

Given lines are 2x+3y−5=0----1x−y+4=0---26x−4y+1=0------3 The slope of the line ax+by+c=0 is −ab Observing the equations Options 1  and 3 their siopes are m1=−23,m3=32, whose product is -1Since the product of slopes of two sides is -1, the triangle formed by the given three lines is right angled triangle. The slope of the second line is m2=1If be the acute angle between (Options: 1) and (2) tanθ=m1−m21+m1m2=−23−11−23=−5≠1 tan 45=1Triangle is not isosceles; it is only right-angled triangle