2.1 Graphing, Distance

Using the Distance Formula

The Distance Formula

Suppose A is ( x_1,   y_1) and B is ( x_2,    y_2)

The distance between points A and B is given by the following formula.

d=sqrt {(x_2-x_1)^2+   (y_2-y_1)^2}

Example: Find the y-coordinate of the points that are 5 units away from the point (3,3) that have an x-coordinate of -1.

5=sqrt {(-1-3)^2+   (y-3)^2}

5=sqrt {(-4)^2+   (y-3)^2}

5=sqrt {16+   (y-3)^2}

5^2=(sqrt {16+   (y-3)^2})^2

25=16+   (y-3)^2

25-16=16-16+   (y-3)^2

9=  (y-3)^2

sqrt{9}=  sqrt{(y-3)^2}

pm 3=  y-3

3 pm 3=  y

3 + 3=  y or 3 - 3=  y

6=  y or 0=  y