Find the distance between each pair of points. Give the exact simplify answer. (3, 8), (9, 10)

Question

The answer has to look like this-

d= _ √1 _

Answer 1

You can use the distance formula, the Distance Between Two Points

to give a simplified answer of

d=√40 = √4*√10

d= 2√10

d=SQRT((x₂ -x₁)²+(y₂ -y₁)²)

d =√(x₂ -x₁)²+(y₂ -y₁)²

Answer 2

Any straight line between two points, with a slope other than infinity or 0, forms a right triangle with the lines between the X-components and Y-components of the points.

In other words this line from (3,8) to (9,10) forms a right triangle with the horizontal line from (3,8) to 9,8) and the vertical line from (9,8) to (9;10).

That make the original line the hypotenuse ("c") and the horizontal and vertical lines "b" and "a" of a Pythagorean triangle.

Therefore if a² + b² = c² it follows that c = √(a² + b²)

In our case the length of the horizontal line ("a") is 6 and the vertical line ("b") is 2.

Therefore c = √(6² + 2²) = √(36 + 4) = √40

Since "c" is the length of our original line connecting the two points, it is also the distance between them.

d = √40