Which line is perpendicular to a line that has a slope of -1/2line ABline CDline FGline HJ

ANSWER

[tex]Line \: \: FG[/tex]


EXPLANATION

In the diagram, line CD passes through
[tex](-4,0) \: \: and \: \: (4,-4).[/tex]


The slope of this line is found using the formula,

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]


We substitute the values to get,

[tex]slope = \frac{ - 4 - 0}{4 - - 4} [/tex]

[tex]slope = \frac{ - 4 }{8} [/tex]

[tex]slope = \frac{ - 1 }{2} [/tex]

So line CD is the line with slope
[tex] - \frac{1}{2} [/tex]

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



Line FG also passes through

[tex](-3,-3) \: and \: (0,3)[/tex]


[tex]slope = \frac{3 - - 3}{0 - - 3} = \frac{6}{3} = 2[/tex]



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

[tex]2 \times \frac{ - 1}{2} = - 1[/tex]

Therefore the correct answer is C