Distance and Triangles on the Coordinate Plane

The video tutorial introduces the concept of calculating distance on the coordinate plane, initially using basic counting methods learned in sixth grade. It progresses to using the Pythagorean theorem to find the distance between two points by forming a right triangle. The tutorial then introduces the distance formula, explaining its derivation and application both graphically and conceptually. The video aims to bridge eighth-grade math skills with introductory algebra concepts, providing a comprehensive understanding of distance calculation.

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

• Draw a line connecting the points

• Count the number of grid squares between the points

• Create a right triangle

• Use the distance formula directly

Why can't we count the distance directly between two points that are not aligned horizontally or vertically?

• It is not a straight line

• The increments are not equal

• The coordinate plane does not allow it

• We need to use the Pythagorean theorem

What theorem is used to find the distance between two points on a coordinate plane?

• Coordinate theorem

• Slope theorem

• Distance theorem

• Pythagorean theorem

In the Pythagorean theorem, what does 'C' represent?

• One of the legs of the triangle

• The midpoint of the line segment

• The hypotenuse of the triangle

• The distance between the points

What is the distance between the points (1, 3) and (-2, 4) using the Pythagorean theorem?

• 3.2 units

• 3.0 units

• 5.0 units

• 4.5 units

What is the formula for finding the distance between two points (x1, y1) and (x2, y2)?

• √((x2 - x1)² + (y2 - y1)²)

• (x2 - x1) + (y2 - y1)

• (x2 + x1) - (y2 + y1)

• √((x2 + x1)² + (y2 + y1)²)

In the distance formula, what do we do after finding the squared differences of the coordinates?

• Add them together

• Subtract them

• Multiply them

• Divide them

What is the final step in using the distance formula?

• Take the square root of the sum

• Square the result

• Subtract the coordinates

• Add the coordinates

Why does the distance formula work conceptually?

• It measures the slope

• It averages the coordinates

• It uses the midpoint formula

• It is based on the Pythagorean theorem

What is the distance between the points (3, 2) and (5, 9) using the distance formula?

• 7.0 units

• 8.1 units

• 6.5 units

• 7.3 units