Question

product of two lines equal to -1 then the two lines are perpendicular. x axis slope is 0 and y axis slope is infinite.how u can prove both are perpendicular

Answer 1

products of slope of two lines = -1

let , y =m1x + c1 and y = m2x + c2
are given two lines .
here slope of 1st line = m1
and 2nd line = m2
then ,
m1 ×m2 = -1

two line perpendicular it means angle between them = 90°

we know, angle between two lines found by
tan∅ = |sum of slopes of lines |/|1+ products of lines|

hence,

tan∅ = | m1 + m2|/| 1 + m1m2|

but a/c to question ,
m1m2 = -1

so, m1m2 +1 = 0

so, tan∅ = ∞
hence , ∅ = 90°
hence, proved when product of two lines = -1 then angle between them is 90° e.g perpendicular to each other

for x and y is co-ordinate axes .
both are perpendicular , and slope of x -axis(m1) = 0 and y -axis(m2) = ∞

we know,
m1× m2 = -1
m1 = -1/m2 = -1/0 = ∞

so, this is satisfied that x-axis and y-axis are perpendicular to each other .

Answer 2

see attachment....hope it will help u