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?

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,

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,

The standard line of equation can be given as,

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,

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;

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"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

where m is slope and is a point on the line.

If we determine the slopes are opposite reciprocal, then we have determine the lines are perpendicular.

y − 4 = −5(x − 1), we see the m is -5.

The slope of this line is -5.

y − 4 = one fifth(x − 5), we see the m is (1/5).

The opposite reciprocal of -5 is 1/5 so theses lines are perpendicular.

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.