Distance and Slope in Geometry

The video tutorial explains how to find the shortest distance between a point and a line. It begins by identifying the point and the line equation, then determines the equation of a perpendicular line passing through the point. The tutorial calculates the intersection of the two lines and uses the distance formula, derived from the Pythagorean theorem, to find the distance between the point and the line.

What is the first step in finding the distance between a point and a line?

• Determine the slope of the line

• Calculate the area under the line

• Identify a perpendicular line through the point

• Find the midpoint of the line

What is the slope of a line perpendicular to y = -1/3x + 2?

• 3

• 1/3

• -1/3

• -3

How do you find the y-intercept of the perpendicular line?

• By substituting the given point into the line equation

• By setting x to zero in the line equation

• By calculating the average of the x-coordinates

• By using the midpoint formula

Where do the two lines intersect?

• At the origin

• At the point (0, 2)

• At the point (-2, -4)

• At the point (2, 0)

What is the distance formula an application of?

• The slope-intercept form

• The quadratic formula

• The Pythagorean theorem

• The midpoint formula

What is the change in the y-direction between the points (-2, -4) and (0, 2)?

• 2

• 8

• 6

• 4

What is the change in the x-direction between the points (-2, -4) and (0, 2)?

• 2

• 0

• 6

• 4

What is the length of the hypotenuse of the right triangle formed by the points (-2, -4) and (0, 2)?

• √20

• √40

• √50

• √10

How can the square root of 40 be simplified?

• 2√10

• 4√10

• 2√5

• √20

What is the final distance between the point (-2, -4) and the line y = -1/3x + 2?

• 4√10

• 10

• √40

• 2√10