Find the distance between the point and the line.Round your answer to four decimal places. Point Line
$( 9,8 ) - 8 x + y - 8 = 0$
A) $d \approx 9.0554$
B) $$d \approx 10.0554$$
C) $d \approx 11.0554$
D) $d \approx 8.0554$
E) $d \approx 12.0554$

Question

Find the distance between the point and the line.Round your answer to four decimal places.​ Point Line
$( 9,8 ) - 8 x + y - 8 = 0$ ​
A)​ $d \approx 9.0554$
B) $$d \approx 10.0554$$
C) $d \approx 11.0554$
D) $d \approx 8.0554$
E) $d \approx 12.0554$

Quizplus · Accepted Answer

The distance $d$ between a point $(x_0, y_0)$ and a line $Ax + By + C = 0$ is given by the formula:$$d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}$$For the given point $(9,8)$ and the line $8x + y - 8 = 0$, we have $A = 8$, $B = 1$, $C = -8$, $x_0 = 9$, and $y_0 = 8$. Plugging these values into the formula gives:$$d = \frac{|8(9) + 1(8) - 8|}{\sqrt{8^2 + 1^2}} = \frac{|72 + 8 - 8|}{\sqrt{64 + 1}} = \frac{72}{\sqrt{65}} \approx 9.0554$$

Find the Distance Between the Point and the Line (9,8)−8x+y−8=0( 9,8 ) - 8 x + y - 8 = 0(9,8)−8x+y−8=0

Find the Distance Between the Point and the Line $( 9,8 ) - 8 x + y - 8 = 0$