Category Archives: Distance

2.1 Graphing, Distance

Using the Distance Formula

March 25, 2017 admin

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

2.1 Graphing, 3.6 Mathematical Models: Building Functions, Distance

Finding the Distance

March 25, 2017 admin

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 distance between points A and B.

Point A is ( 4, -2) and point B is ( -8, 3)

$d=sqrt {(-8-4)^2+ (3-(-2))^2}$

$d=sqrt {(-12)^2+ (3+2)^2}$

$d=sqrt {144+ (5)^2}$

d=sqrt {144+ 25}

d=sqrt {169}

d=13

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