Perpendicular Lines and Distance Concepts

This video tutorial explains how to determine the shortest distance between a point and a line. It begins by introducing the concept of perpendicular line segments as the shortest distance. The video then reviews the slopes of perpendicular lines, emphasizing that they are negative reciprocals. An example problem is presented, demonstrating how to calculate the shortest distance using the distance formula. The tutorial concludes with tips on handling intersection points with non-integer coordinates.

What is the shortest distance between a point and a line?

• A line segment parallel to the x-axis

• A line segment parallel to the y-axis

• A line segment perpendicular to the given line

• A line parallel to the given line

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

• They are undefined

• They are equal

• They are negative reciprocals

• They are both zero

If a line has a slope of 2/3, what is the slope of a line perpendicular to it?

• -3/2

• 3/2

• 2/3

• -2/3

What is the slope of a line perpendicular to a vertical line?

• Zero

• Undefined

• One

• Negative one

In the example, what are the coordinates of the given point?

• (0, 0)

• (2, -4)

• (1, -6)

• (3, -5)

How do you find the slope of a line given two points?

• Subtract the y-coordinates and divide by the difference in x-coordinates

• Add the x-coordinates

• Multiply the coordinates

• Subtract the x-coordinates and divide by the difference in y-coordinates

What is the negative reciprocal of a slope of -2?

• -2

• 1/2

• -1/2

• 2

What is the distance between the points (1, -6) and (3, -5)?

• Square root of 5

• Square root of 10

• 2

• 3

What is the formula used to calculate the distance between two points?

• Equation of a line

• Distance formula

• Midpoint formula

• Slope formula

What might you need to do if the intersection coordinates are not integers?

• Ignore the coordinates

• Estimate the coordinates

• Use a calculator

• Solve a system of equations