Find the distance between the point and the line.Round your answer to four decimal places. Point Line
$( 2,3 ) \quad x - y = 2$
A) $d \approx 6.6569$
B) $d \approx 7.6569$
C) $d \approx 4.6569$
D) $d \approx 8.6569$
E) $d \approx 5.6569$

Question

Find the distance between the point and the line.Round your answer to four decimal places.  Point Line
$( 2,3 ) \quad x - y = 2$ 
A) $d \approx 6.6569$
B) $d \approx 7.6569$
C) $d \approx 4.6569$
D) $d \approx 8.6569$
E) $d \approx 5.6569$

Quizplus · Accepted Answer

The distance from a point $(x_1, y_1)$ to a line $Ax + By + C = 0$ is given by $\frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$. For the line $x - y = 2$, rewrite it as $x - y - 2 = 0$. Using the formula, the distance is $\frac{|2 - 3 - 2|}{\sqrt{1^2 + (-1)^2}} = \frac{|-3|}{\sqrt{2}} \approx 5.6569$.

Find the Distance Between the Point and the Line (2,3)x−y=2( 2,3 ) \quad x - y = 2(2,3)x−y=2

Find the Distance Between the Point and the Line $( 2,3 ) \quad x - y = 2$