Distance formula

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

• y=mx+b

• a² + b² = c²

• y₂-y₁

• x₂-x₁

Answer explanation

In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

The hypotenuse is the longest side, and it is opposite to the 90° angle.

How is the base of the triangle calculated between points (3, -4) and (6, 0)?

• Subtracting th x coordinates (6 -3)

• Subtracting the y coordinates (-4 - 0)

• Adding the x coordinates (6 + 3)

• Adding the y coordinates (-4 + 0)

Answer explanation

An ordered pair (x, y) is defined as the coordinates of a point such that “x” is the x-coordinate and “y” is the y-coordinate.

For point (6,0)

6 is the x-coordinate, and 0 is the y-coordinate.

For point (3,-4)

3 is the x-coordinate, and -4 is the y-coordinate.

The horizontal change, or change in x (Δx), is the difference between the two x -coordinates, or 6 - 3.

What does the hypotenuse in the context of the video represent?

• The base of the triangle

• The height of the triangle

• The area of the triangle

• The distance between two points

Answer explanation

You can use the Pythagorean Theorem to find the distance between two points.

The distance between the two points is the hypotenuse (c).

a² + b² = c²

3² + 4² = c²

9 + 16 =c²

25 = c²

√25 = √c²

5 = c

What is the correct expression for the distance formula?

• (x² - x¹) + (y² - y¹)

• (x² + x¹)² + (y² + y¹)²

Answer explanation

What is the distance between the points (-6, -4) and (1, 7) as calculated in the video?

• 11 units

• 13.04 units

• 7 units

• 25 units

What are the coordinates for point A?

Hint: (x,y)

What are the coordinates for point B?

Hint: (x,y)

What is the horizontal change/change in x?

• 1

• 2

• 4

• -2

Answer explanation

The change in x (Δx) is

4-2 = 2

What is the vertical change/change in y?

• 1

• 2

• 3

• -2

Answer explanation

The vertical chance (Δy) is 3 - 1 = 2

What is the distance between points A and B?

(Round to the nearest hundredth)

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The distance between point A and point B is about  _______ units.

Answer explanation