Question

The equation of four lines are given. Identify which lines are perpendicular.

Line one: y= -1
Line two: y= - 1/2x-2
Line three: x= -4
Line four: y+3=2(x-2)
A.) Lines 2 and 4 are perpendicular
B.) none of the lines are perpendicular
C.) Lines 1 and 3 are perpendicular and lines 2 and 4 are perpendicular.
D.) Lines 1 and 3 are perpendicular.

Answer 1

Lines 2 and four r perpendicular I think

Answer 2

Answer: A.) Lines 2 and 4 are perpendicular

Explanation:

Two lines are said to be perpendicular if the product of their slope gives - 1 . That is , if
`m_(1)` is the slope of the first line and
`m_(2)` is the slope of the second line , if the two lines are perpendicular , then :

`m_(1)`
`m_(2)` = -1 , which can also be written as ;

`m_(1)` = -1 /
`m_(2)`.

The equation of line in slope intercept form is given as :

y = mx + c , where m is the slope and c is the y - intercept.

Line one : y = - 1 , comparing with the equation of line in slope intercept form , it means line one has no slope

Line two : y = -1/2x - 2 , it has a slope of - 1/2

Line 3 : x = -4 , has no slope

Line 4 : y + 3 = 2 ( x - 2 )

Writing this in slope intercept form , we will make y the subject of the formula.

y + 3 = 2x - 4

y = 2x -4 - 3

y = 2x - 7

This means that the slope of line 4 is 2.

Comparing line two and line four to check if they are perpendicular

- 1/2 x 2 = - 1 , surely , it obeys the perpendicularity rule , this means that line 2 and 4 are perpendicular