Calculate the requested distance.
-The distance from the point S(-10, -4, -6) to the plane -9x + 2y + 6z
A) $\frac { 122 } { 11 }$
B) $\frac { 42 } { 11 }$
C) $\frac { 122 } { 121 }$
D) $\frac { 42 } { 121 }$

Question

Calculate the requested distance.
-The distance from the point S(-10, -4, -6) to the plane -9x + 2y + 6z  
A) $\frac { 122 } { 11 }$
B) $\frac { 42 } { 11 }$
C) $\frac { 122 } { 121 }$
D) $\frac { 42 } { 121 }$

Quizplus · Accepted Answer

To find the distance from a point to a plane, we use the formula:

distance = $\frac {|ax_0 + by_0 + cz_0 + d| }{\sqrt{a^2+b^2+c^2}}$

where (x0, y0, z0) is the point, a, b, and c are the coefficients of the plane, and d is the constant term.

Here, the coefficients of the plane are -9, 2, and 6, and the constant term is 0 (since the plane passes through the origin). Plugging in the coordinates of the point S, we get:

distance = $\frac {|(-9)(-10) + (2)(-4) + (6)(-6) + 0| }{\sqrt{(-9)^2+(2)^2+(6)^2}}$

= $\frac {122 } {11}$

Therefore, the best choice is B.

Calculate the Requested Distance 12211\frac { 122 } { 11 }11122​

Calculate the Requested Distance $\frac { 122 } { 11 }$