Is the line through(-2,3) and(4,1)perpendicular to the line 3x=y+1?if yes then does the line 3x+1 bisect the join of(-2,3) and(4,1)

 

Asked by hrmeenal24 | 9th Feb, 2020, 11:19: AM

Expert Answer:

let space straight A open parentheses negative 2 comma 3 close parentheses space and space straight B left parenthesis open parentheses 4 comma 1 right parenthesis close parentheses
equation space of space AB equals
straight y minus 3 equals fraction numerator 1 minus 3 over denominator 4 plus 2 end fraction open parentheses straight x plus 2 close parentheses
straight x plus 3 straight y equals 7... open parentheses 1 close parentheses
given space line
3 straight x minus straight y equals 1... left parenthesis 2 right parenthesis
slope space of space given space line space is space 3
they space are space perpendicular space to space each space other space since space the space product space of space slopes space is space minus 1
solving space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis
points space of space intersection space left parenthesis 1 comma 2 right parenthesis
now space the space mid space points space of space AB equals open parentheses fraction numerator negative 2 plus 4 over denominator 2 end fraction comma fraction numerator 3 plus 1 over denominator 2 end fraction close parentheses equals open parentheses 1 comma 2 close parentheses space which space is space same space as space the space intersection space point

Answered by Arun | 9th Feb, 2020, 11:34: AM