Perpendicular Lines and Gradients

The video tutorial explains how to find the equation of a line that is perpendicular to a given line. It starts by identifying the need for the gradient of the perpendicular line to be the negative reciprocal of the original line's gradient. The tutorial then demonstrates how to use a given point to solve for the y-intercept, ultimately deriving the equation of the new line.

What is the first step in solving the problem of finding a perpendicular line's equation?

• Identify the y-intercept of the given line.

• Find the gradient of the given line.

• Determine the length of the line segment.

• Calculate the midpoint of the line.

What is the gradient of the line y = 2x + 3?

• 1

• -1/2

• 2

• 3

How do the gradients of two perpendicular lines relate to each other?

• They are equal.

• They are both zero.

• They are negative reciprocals.

• They are both positive.

What is the result of multiplying the gradients of two perpendicular lines?

• -1

• 0

• 2

• 1

If a line has a gradient of 2, what is the gradient of a line perpendicular to it?

• 2

• -1/2

• -2

• 1/2

What is the purpose of finding the negative reciprocal of a gradient?

• To find the y-intercept

• To calculate the midpoint

• To find the gradient of a perpendicular line

• To determine the length of the line

What is the equation form used to represent the new line with a known gradient?

• y = -1/2x + C

• y = ax^2 + bx + c

• y = x^2 + C

• y = mx + b

What is the equation of a line with a gradient of -1/2 and passing through the origin?

• y = -1/2x

• y = 2x

• y = x - 1/2

• y = -x + 1/2

Which point is used to substitute into the equation to find the y-intercept?

• (2, 3)

• (4, 7)

• (1, 1)

• (0, 0)

What is the value of y when x is 4 in the equation y = -1/2x + C?

• 4

• 9

• 7

• 2