Question

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?

Answer 1

Answer:

Segments AB and CD are perpendicular to each other.

Step-by-step explanation:

If you were to convert line segments AB and CD into slope-intercept form(y=mx+b), you would get y=-5x+1 for AB and y=1/5x-5.

Any line with a slope that is flipped-oppisite (-5/1 to -1/5 to1/5)

of another line must be perpendicular to each other. It doesn't have to have the same y-intercept, it just makes the intersecting point different.

Answer 2

Answer:

"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.

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

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

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

The slope of this line is -5.

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

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.