Midpoint and Distance Formulas Explained

This video tutorial covers the distance and midpoint formulas, explaining their derivations and applications. It begins with an introduction to the distance formula using a graph and the Pythagorean theorem. The tutorial then delves into the details of calculating distances between points on a coordinate plane. Following this, the midpoint formula is introduced, emphasizing its use in finding the center between two points. The video concludes with a discussion on perpendicular bisectors, including how to find their equations using slopes and midpoints.

What is the first step in finding the distance between two points on a coordinate plane?

• Identify the midpoint of the points

• Use the Pythagorean theorem

• Count the number of units between the points

• Draw a horizontal line

When using the distance formula, what should you do after squaring the differences of the coordinates?

• Multiply the squared differences

• Subtract the squared differences

• Add the squared differences

• Divide the squared differences

In the distance formula, why does it not matter if you get a negative number when subtracting coordinates?

• Because you square the differences, making them positive

• Because you multiply the differences

• Because you always add the coordinates

• Because you take the absolute value

What is the distance between the points (-2, -4) and (3, 4)?

• Square root of 82

• Square root of 25

• Square root of 64

• Square root of 89

What is the midpoint of the points (-5, -10) and (7, -30)?

• (2, -15)

• (0, -20)

• (1, -10)

• (1, -20)

How do you find the midpoint of two numbers?

• Divide the numbers and add 2

• Multiply the numbers and divide by 2

• Add the numbers and divide by 2

• Subtract the numbers and divide by 2

What is the slope of a line perpendicular to a line with a slope of 2/3?

• 2/3

• -3/2

• 3/2

• -2/3

What is the equation of a line that is perpendicular to a line with a slope of 1/4 and passes through the point (1, 5)?

• y = 1/4x - 5

• y = -4x + 9

• y = 4x + 1

• y = -1/4x + 5

What is the midpoint of the line segment with endpoints (8, 1) and (-7, 1)?

• (0.5, 0.5)

• (1, 0.5)

• (1, 1)

• (0.5, 1)

What is the equation of a vertical line that passes through the point (4, 6)?

• x = 4

• y = 4

• x = 6

• y = 6