2F Perpendicular

Front

What is the definition of a perpendicular line?

Back

A perpendicular line is a line that intersects another line at a right angle (90 degrees).

Front

How do you determine if two lines are perpendicular using their slopes?

Back

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

Front

What is the slope of a line that is perpendicular to a line with a slope of 3?

Back

The slope of a line perpendicular to a line with a slope of 3 is -1/3.

Front

If line A has a slope of 2, what is the equation of a line perpendicular to it that passes through the point (1, 2)?

Back

The equation is y - 2 = -1/2(x - 1).

Front

What is the relationship between perpendicular lines in a coordinate plane?

Back

Perpendicular lines in a coordinate plane intersect at right angles and have slopes that are negative reciprocals of each other.

Front

Define the term 'negative reciprocal' in the context of slopes.

Back

The negative reciprocal of a number is obtained by flipping the fraction and changing the sign. For example, the negative reciprocal of 4 is -1/4.

Front

What is the geometric significance of perpendicular bisectors?

Back

A perpendicular bisector of a segment is a line that divides the segment into two equal parts at a right angle.

Front

How can you find the equation of a perpendicular bisector given two endpoints?

Back

1. Find the midpoint of the segment. 2. Determine the slope of the segment. 3. Use the negative reciprocal of that slope for the perpendicular bisector.

Front

What is the formula for the distance between two points in a coordinate plane?

Back

The distance d between points (x1, y1) and (x2, y2) is given by d = √((x2 - x1)² + (y2 - y1)²).

Front

Explain how to use the Pythagorean theorem in relation to perpendicular lines.

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.