Question

find the slope of a line perpendicular to the line which passes through each pair of the following points
i) (0,8) and (-5,2)
ii) (1,-11)and (5,2)
iii) (-k,h) and (b,-f)
iv) (x1,y1) and (x2,y2)​

Answer 1

Answer:

1. 2/13

2. -1/10

3. k-f/h-b

4. x1 -x2/ y2 - y1

Step by Step explanation

the equation of slope m of a line is

m = y2 - y1/ x2 - x1

and the slope of a line perpendicular to the given line is given by

m' = -1/m

Answer 2

Answer:

i) slope of the given line = (y2- y2)/(x2-x1)

= -6/-5

= 6/5

if two lines are perpendicular, we write their slopes as : m1 × m2 = -1

Hence, m× 6/5 = -1

m = -5/6

ii) m1 = 2-(-11)/5-1

= 13/4

m1×m2= -1

m2 = -4/13

iii) m1 = (-f-h)/b-(-k)

= -(f+h)/b+k

Hence,

m1×m2= -1

m2 = (b+k)/(f+h)

iv) given slope = (y2-y1)/(x2-x1)

slope of line perpendicular to it

= -(x2-x1)/(y2-y1)

Hope it helps!