HarleyQuinn619
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HURRY PLEASE WHOEVER ANSWERS FIRST WILL BE THE BRAINLIEST!!!
Which statement best explains the relationship between lines FG and HJ?

A.They are perpendicular because their slopes are equal.
B.They are perpendicular because their slopes are negative reciprocals.
C.They are not perpendicular because their slopes are equal.
D.They are not perpendicular because their slopes are not negative reciprocals.

HURRY PLEASE WHOEVER ANSWERS FIRST WILL BE THE BRAINLIEST Which statement best explains the relationship between lines FG and HJ AThey are perpendicular because class=

Respuesta :

col08
The answer to this question is B. They are perpendicular because their slopes are negative reciprocals.

Two lines can be perpendicular if they make a 90 degree angle and/or their slopes are negative reciprocals.
calculista

we know that

If two lines are perpendicular then, the product of their slopes is equal to minus one, that means that their slopes are negative reciprocals

so

[tex]m1*m2=-1[/tex]

Step [tex]1[/tex]

Find the slope of the line HJ

[tex]H(-4,-2)\\J(0,4)[/tex]

we know that

the slope between two points is equal to

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

substitute the values

[tex]m1=\frac{(4+2)}{(0+4)}[/tex]

[tex]m1=\frac{(6)}{(4)}[/tex]

[tex]m1=\frac{3}{2}[/tex]

Step [tex]2[/tex]

Find the slope of the line HJ

[tex]F(-4,1)\\G(0,-2)[/tex]

we know that

the slope between two points is equal to

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

substitute the values

[tex]m2=\frac{(-2-1)}{(0+4)}[/tex]

[tex]m2=\frac{(-3)}{(4)}[/tex]

[tex]m2=-\frac{3}{4}[/tex]

Step [tex]3[/tex]

Verify if the two lines are perpendicular

[tex]m1=\frac{3}{2}[/tex]

[tex]m2=-\frac{3}{4}[/tex]

Find the product m1 by m2

[tex]\frac{3}{2}*-\frac{3}{4}=-\frac{9}{8}[/tex]

so

[tex]-\frac{9}{8}\neq -1[/tex] --------> the slopes are not negative reciprocals

therefore

the answer is the option

D.They are not perpendicular because their slopes are not negative reciprocals

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