Question

Find the equation of a line through (1,1) which

isperpendicular to a line through (1,3) and (2,5).

Answer 1

`y=(-1)/(2)x+(3)/(2)`

Explanation:

Point on a line is (1,3) and (2,5).

`slope=(y_2-y_1)/(x_2-x_1) =(5-3)/(2-1) =2`

slope of given line is 2

slope of perpendicular lines are negative reciprocal of one another

slope of perpendicular line is -1/2

slope = -1/2 (1,1)

`y-y_1=m(x-x_1)`

`y-1=(-1)/(2)(x-1)`

`y-1=(-1)/(2)x+(1)/(2))`

add 1 on both sides

`y=(-1)/(2)x+(3)/(2)`