Using Properties of Perpendicular Lines

The shortest distance between a point and a line is the length of the perpendicular segment from the point to the line. In this case, that is

\overline{A B} .

The distance from

A

to

B

can be calculated using the distance formula.

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

By substituting the points for

A

and

B

into the formula we can calculate the distance

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

(3, 0)

&

(0, 1)

A Y = (3 - 0)^{2} + (0 - 1)^{2}

Simplify right-hand side

SubTermsSubtract terms

A Y = 3^{2} + (- 1)^{2}

CalcPowCalculate power

A Y = 9 + 1

AddTermsAdd terms

A Y = 10

CalcRootCalculate root

A Y = 3.16227

RoundDecRound to

A Y \approx 3.2

Using Properties of Perpendicular Lines 1.3 - Solution