Understanding Perpendicular Bisectors

This video tutorial explains how to determine the perpendicular bisector of a segment on the coordinate plane. It covers the properties of perpendicular bisectors, such as dividing a segment into two congruent parts and forming right angles. The tutorial demonstrates how to find the midpoint of a segment and calculate the slope, including the concept of negative reciprocals. Finally, it shows how to derive the equation of the perpendicular bisector using the point-slope form and verifies it by graphing.

What is one of the key properties of a perpendicular bisector on a coordinate plane?

• It divides a segment into two congruent parts.

• It forms an acute angle with the segment.

• It divides a segment into two unequal parts.

• It forms an obtuse angle with the segment.

What is the relationship between the slopes of two perpendicular lines?

• Their slopes are both zero.

• Their slopes are positive reciprocals.

• Their slopes are negative reciprocals.

• Their slopes are equal.

What is the result when you multiply the slopes of two perpendicular lines?

• 1

• 0

• -1

• 2

What is the first step in determining the equation of a perpendicular bisector?

• Determine the midpoint of the segment.

• Find the slope of the bisector.

• Graph the segment.

• Calculate the y-intercept.

How do you find the x-coordinate of the midpoint of a segment?

• Add the x-coordinates and divide by two.

• Divide the x-coordinates by two.

• Subtract the x-coordinates and divide by two.

• Multiply the x-coordinates and divide by two.

What is the slope of the segment with endpoints (-3, -4) and (5, 0)?

• -1

• 1

• 1/2

• -1/2

What is the slope of a line that is perpendicular to a line with a slope of 1/2?

• -1/2

• 2

• 1/2

• -2

Which form is used to find the equation of a line given a point and a slope?

• Standard form

• Point-slope form

• Quadratic form

• Slope-intercept form

What is the y-intercept of the line with the equation y = -2x?

• 0

• 1

• 2

• -2

How can you verify that a line is the perpendicular bisector of a segment?

• By confirming it has a positive slope.

• By ensuring it forms a right angle with the segment and bisects it.

• By verifying it is parallel to the segment.

• By checking if it passes through the origin.