Question

Select the correct answer from each drop-down menu to complete the statement. the two new paths will be to each other because their slopes are

Answer 1

The two new paths will be perpendicular to each other because their slopes are negative reciprocals.

1. Perpendicular:

• In geometry, two lines are perpendicular if they intersect at a right angle, forming 90 degrees between them.
• In the context of paths or lines, being perpendicular means that they cross each other at a right angle.

Alternative Options: Parallel, intersecting, oblique.

2. Negative Reciprocals:

• The slope of a line represents its steepness. If the slope of one line is
  `\(m\)`, the negative reciprocal is
  `\(-1/m\)`.
• For example, if one line has a slope of 2, its negative reciprocal is
  `\(-1/2\)`.

Alternative Options: Equal, parallel, undefined (for vertical lines).

Putting it all together:

"The two new paths will be **perpendicular** to each other because their slopes are **negative reciprocals**. This means that the lines will intersect at right angles, and the steepness of one path is the negative reciprocal of the other."

Alternative Statement:

"The two new paths will be **parallel** to each other because their slopes are **equal**. This means that the lines will never intersect and maintain a constant separation distance."