Exploring the Distance Formula in Geometry

In this video, Mr. Backberg explains the distance formula, which is used to find the length between two points on a coordinate plane. The video covers the formula's derivation using the Pythagorean theorem, provides step-by-step examples, and offers practice problems to reinforce understanding. The video also includes tips on handling negative values and using a calculator for decimal approximations.

What is the primary purpose of the distance formula?

• To find the area of a triangle

• To find the length of segments in the coordinate plane

• To determine the midpoint of a segment

• To calculate the slope of a line

Which theorem is used to help find side lengths in a right triangle?

• Remainder theorem

• Fundamental theorem of calculus

• Binomial theorem

• Pythagorean theorem

To find the length of a horizontal segment, which values do we focus on?

• W values

• X values

• Z values

• Y values

What is the formula for the length of a vertical segment?

• Absolute value of x2 - x1

• Square root of (y2 - y1)^2

• Square root of (x2 - x1)^2

• Absolute value of y2 - y1

In the distance formula, what do we do with the differences in x and y values?

• Add them together

• Subtract them

• Square them and add

• Multiply them

What is the distance formula?

• d = (x2 - x1) + (y2 - y1)

• d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

• d = (x2 - x1)^2 + (y2 - y1)^2

• d = sqrt((x2 - x1) + (y2 - y1))

If point A is (-2, -1) and point B is (3, 2), what is the distance between them?

• 5.83

• 8.54

• 6.08

• 7.21

For the points (-1, 3) and (5, 2), what is the distance between them?

• 8.54

• 5.83

• 6.08

• 7.21

What is the distance between the points (3, -5) and (7, -2)?

• 5

• 4

• 7

• 6

What is the square root of 25?

• 3

• 4

• 5

• 6