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

To find the distance between a point and a line, we need to use the formula:

$$d=\frac{|Ax+By+C|}{\sqrt{A^2+B^2}}$$

where $A$, $B$, and $C$ are the coefficients of the equation of the line $Ax+By+C=0$, and $(x,y)$ are the coordinates of the point. In this case, the equation of the line is $x-y=2$, or $x-y-2=0$. So, $A=1$, $B=-1$, and $C=-2$. The point is $(2,3)$. Substituting into the formula, we get:

$$d=\frac{|1\cdot 2+(-1)\cdot 3+(-2)|}{\sqrt{1^2+(-1)^2}}\approx 5.6569$$

Therefore, the best choice is E, because it is closest to this result (rounded to four decimal places).

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