Parallel and Perpendicular Lines

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never meet. They have the same slope but different y-intercepts.

Front

What are perpendicular lines?

Back

Perpendicular lines are lines that intersect at a right angle (90 degrees). The slopes of two perpendicular lines are negative reciprocals of each other.

Front

How do you determine if two lines are parallel based on their equations?

Back

Two lines are parallel if they have the same slope in their slope-intercept form (y = mx + b).

Front

How do you determine if two lines are perpendicular based on their equations?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.

Front

What is the relationship between the circumcenter and orthocenter in an obtuse triangle?

Back

In an obtuse triangle, the circumcenter lies outside the triangle, while the orthocenter also lies outside the triangle.

Front

What is the equation of a line parallel to y = -3 that passes through the point (2,6)?

Back

The equation is y = 6, as parallel lines have the same y-value.

Front

What is the significance of the slopes of lines in determining their relationship?

Back

The slope indicates the steepness and direction of a line; it is crucial for determining if lines are parallel, perpendicular, or neither.

Front

What is the slope of the line y = 4x + 2?

Back

The slope is 4.