Find the distance between each pair of points. Leave your answer in radical form.Show all work and solutions for # 1, 2 and 3 in the space below.

Question

https://studylib.net/doc/7055018/activity-1.1.4-using-the-distance-formula

Answer 1

Let one point be (x1, y1) and the other point (x2, y2)

Find the vertical and horizontal differences between the two points:

Vertical: difference of the y’s ( y2 - y1)

Horizontal: difference of the x’s (x2 - x1)

The vertical and horizontal differences form the legs of a right triangle

The distance from one point to the other is the hypotenuse of the right triangle

Pythagorean theorem states: The sum of the squares of the legs is equal to the square of the hypotenuse

Using this: (x2 - x1)^2 + (y2 - y1)^2 = hypotenuse^2. (The symbol ^ means exponent)

Squaring both sides to get the hypotenuse

Square root of [ (x2 - x1)^2 + (y2 - y1)^2 ] = the distance

This is the distance formula and can be used for any values of x and y.