Analytic Geometry Problem

Geometry Level 1

In the graph above, the blue straight line is the function $y=x$ . What is the smaller distance of the point $A$ to the straight line $y=x$ ?

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3\sqrt{2}

\sqrt{2}

3\sqrt{3}

2\sqrt{2}

1 solution

Andronikus Lumembang
Jan 19, 2015

Distances between line of function $ax + by + c = 0$ to the point $(x_1,y_1)$ can be described as :

$D = \frac{ax_1 + by_1 + c}{\sqrt{a^2 + b^2}}$

$D = \frac{-1.1 + 1.5 + 0}{\sqrt{(-1)^2 + 1^2}} = \boxed{2\sqrt2}$

P.S : Distance always means the smallest values