Mathematics, 13.07.2019 08:10, haidenmoore92

Segment ab is on the line y − 4 = −5(x − 1), and segment cd is on the line y − 4 = one fifth(x − 5). which statement proves the relationship of segments ab and cd?

Answers: 2

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Answers

The slope of the gradient of the line is a number that describe both the direction and the steepness of the line. The given question they are perpendicular because they have slopes that are opposite reciprocals of -5 and one fifth. Thus option 2 is the correct option.

Given-

Equation of the line is,

y-4=-5(x-1)

What is the slope of the line?

The slope of the gradient of the line is a number that describe both the direction and the steepness of the line

Statement given in the question are,

They are perpendicular because they have slopes that are opposite reciprocals of 5 and negative one fifth.They are perpendicular because they have slopes that are opposite reciprocals of -5 and one fifth.They are parallel because they have the same slope of 5.They are parallel because they have the same slope of negative one fifth.

The standard line of equation can be given as,

(y-y_1)=m(x-x_1)

Compare the above equation with the given equation we get the of m is -5.

Thus the slope of the given line is -5. The opposite reciprocal of -5 is 1/5.

Put in the equation,we get,

$(y-4)=\dfrac{1}{5}(x-5)$

Hence, for the given question they are perpendicular because they have slopes that are opposite reciprocals of -5 and one fifth. Thus option 2 is the correct option.

Learn more about the slope of the line here;

link

answered: anondriap

"They are perpendicular because they have slopes that are opposite reciprocals of −5 and one fifth."

Step-by-step explanation:

These lines are both in a form called point-slope form which is

y-y_1=m(x-x_1) where m is slope and (x_1,y_1) is a point on the line.