Question

There is a geometric theorem that says "If two lines in a plane are

perpendicular to the same line, they are parallel to each other." Explain why this
is true by writing and comparing equations for two different lines that are
perpendicular to y=-1/3x

Answer 1

This is true as if the lines are perpendicular, they intersect the other line at a right angle. That means that if they are both perpendicular to the same line, they have the same slope and are parallel to each other.

Explanation:

If one line is y=-1/3x, then the perpendicular lines must be the negative reciprocal. Therefore, they would be, y=1/3x. They would both have that as their slope which would make them parallel to each other. This is the same for any two lines that are both perpendicular to the same line.

Answer 2

Explanation:

For a line to be perpendicular to another line, its slope must be the negative inverse of the original line’s.

For example, the negative inverse of 3x is -1/3 x.

The line y = 3x is perpendicular to y = -1/3 x. Any line with a slope of 3x is perpendicular regardless of its y-intercept.

Plotted on the graph are the equations:

Y = 3x

Y = 3x + 3

Y = - 1/3 x

As you can see, the lines with the slope of 3x are perpendicular to the third line regardless of their y-intercepts. Only slope matters in regards to parallel and perpendicular lines.