Distance Formula

The video tutorial explains the concept of distance in both everyday contexts and on a coordinate plane. It introduces the use of Pythagoras' theorem to calculate the distance between two points on a graph, initially using specific examples. The tutorial then generalizes this approach to derive the distance formula, which can be applied to any two points on a plane. The video concludes by verifying the formula with examples, demonstrating its practical application.

What is the distance between two points A(0, 4) and B(3, 0) on the coordinate axes?

• 5 units

• 6 units

• 4 units

• 3 units

In a right triangle formed by points A(4, 5) and B(-3, -4), what is the approximate length of the hypotenuse?

• 7.5 units

• 9.8 units

• 13.2 units

• 11.4 units

What is the general formula for calculating the distance between two points (X1, Y1) and (X2, Y2) on a plane?

• D = |X2 - X1| + |Y2 - Y1|

• D = (X2 - X1) + (Y2 - Y1)

• D = (X2 - X1)^2 + (Y2 - Y1)^2

• D = √((X2 - X1)^2 + (Y2 - Y1)^2)

Why is the square of X1 - X2 the same as the square of X2 - X1?

• Because addition is commutative

• Because the square of a number is always positive

• Because multiplication is associative

• Because subtraction is commutative

Using the distance formula, what is the distance between points P(4, 6) and Q(6, 1)?

• √5 units

• 10 units

• 5√5 units

• 5 units

What is the significance of the distance formula in coordinate geometry?

• It is used to determine the area of a triangle

• It provides a method to calculate the distance between any two points on a plane

• It is used to calculate the slope of a line

• It helps in finding the midpoint of a line segment

Which theorem is used to derive the distance formula?

• Fermat's Last Theorem

• Pythagorean Theorem

• Thales' Theorem

• Euclid's Theorem