Question

what is the distance between the points (-2, -11) and (-2, 23) in the coordinate plane?
a. 32 units
b. 34 units
c. 12 units

Explanation:

Step1: Identify the coordinates

The two points are $(-2,-11)$ and $(-2,23)$. The $x$-coordinates are the same ($x_1 = x_2=-2$).

Step2: Use the distance formula for points with same x - coordinate

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ when $x_1 = x_2$ is $d=\vert y_2 - y_1\vert$. Here, $y_1=-11$ and $y_2 = 23$. So $d=\vert23-(-11)\vert=\vert23 + 11\vert$.

Step3: Calculate the absolute - value

$\vert23 + 11\vert=\vert34\vert = 34$.

Answer:

B. 34 units