Question

On a coordinate plane, 2 lines are shown. Line C D has points (negative 2, 4) and (0, negative 4). Line F G has points (negative 4, 0) and (4, 2).
Which statement best explains the relationship between lines CD and FG?

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

Answer 1

Answer:

They are perpendicular because their slopes are negative reciprocals.

Step-by-step explanation:

Answer 2

The statement best explains the relationship between lines CD and FG is option (B) they are perpendicular because their slopes are negative reciprocals is the correct answer.

What is equation of a line?

The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.

For the given situation,

The equation of line is

$(y-y1)=(\frac{y2-y2}{x2-x1} )(x-x1)$

Line C D has points (x1,y1) is ( -2, 4) and (x2,y2) is (0, -4).

So the line CD is

⇒ $(y-4)=(\frac{-4-4}{0-(-2)} )(x-(-2))$

⇒ $(y-4)=(\frac{-8}{2} )(x+2)$

⇒ $(y-4)=-4(x+2) --------- (1)$

The general equation of line in slope intercept form is

$y=mx+c$

Here , $m1=-4$

Line F G has points (x1,y1) is ( -4, 0) and (x2,y2) is (4, 2).

So the line FG is

⇒ $(y-0)=(\frac{2-0}{4-(-4)} )(x-(-4))$

⇒ $y=(\frac{2}{8} )(x+4)$

⇒ $y=\frac{1}{4} (x+4)$

Here $m2=\frac{1}{4}$

Thus the slope, $-m1=\frac{1}{m2}$

Hence we can conclude that the statement best explains the relationship between lines CD and FG is option (B) they are perpendicular because their slopes are negative reciprocals is the correct answer.

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