Perpendicular Bisectors and Gradients

The video tutorial explains how to find the equation of a perpendicular bisector of a line segment joining two points. It covers plotting points, drawing lines, calculating midpoints, and finding gradients. The tutorial also demonstrates how to determine the perpendicular gradient and substitute it into the equation of a straight line. Several example problems are solved to illustrate the process, and the video concludes with tips for exams.

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

• Find the midpoint of the line segment

• Identify the endpoints of the line segment

• Calculate the gradient of the line segment

• Draw the line segment

When plotting points A(1,4) and B(5,-6), what is the next step?

• Find the midpoint of the line segment

• Draw the line segment connecting the points

• Calculate the distance between the points

• Determine the gradient of the line segment

What does a perpendicular bisector do to a line segment?

• Extends it indefinitely

• Divides it into three equal parts

• Runs parallel to it

• Cuts it into two equal parts at a right angle

How do you find the midpoint of a line segment with endpoints (1,4) and (5,-6)?

• (3, -1)

• (2, 1)

• (2, -1)

• (3, 1)

What is the formula for calculating the gradient of a line segment?

• (x1 + x2) / 2

• (y2 - y1) / (x2 - x1)

• (x2 - x1) / (y2 - y1)

• (y1 + y2) / 2

If the gradient of a line is -5/2, what is the gradient of its perpendicular bisector?

• -5/2

• 5/2

• -2/5

• 2/5

What is the purpose of simplifying the equation of a perpendicular bisector?

• To determine the endpoints of the bisector

• To make it easier to graph

• To prepare for solving simultaneous equations

• To find the length of the bisector

For points C(7,4) and D(-3,2), what is the midpoint?

• (4, 3)

• (3, 2)

• (2, 3)

• (2, 4)

What is the gradient of the line segment CD with points C(7,4) and D(-3,2)?

• -1/5

• 1/5

• -5

• 5

For points E(0,-3) and F(5,-2), what is the perpendicular gradient?

• -5

• 5

• 1/5

• -1/5