Question

Which line is perpendicular to a line that has a slope of -1/2

line AB

line CD

line FG

line HJ

Answer 1

ANSWER


`Line \: \: FG`


Step-by-step explanation

In the diagram, line CD passes through

`(-4,0) \: \: and \: \: (4,-4).`


The slope of this line is found using the formula,


`slope=(y_2-y_1)/(x_2-x_1)`


We substitute the values to get,


`slope = ( - 4 - 0)/(4 - - 4)`


`slope = ( - 4 )/(8)`


`slope = ( - 1 )/(2)`

So line CD is the line with slope

`- (1)/(2)`

From the graph we can see clearly that, the only line that is perpendicular to CD is line FG.



Line FG also passes through


`(-3,-3) \: and \: (0,3)`



`slope = (3 - - 3)/(0 - - 3) = (6)/(3) = 2`



We can verify that the product of these two slopes is negative 1.


`2 * ( - 1)/(2) = - 1`

Therefore the correct answer is C