Question

1. (-11, 7) and (-11, -2)

Explanation:

Step1: Identify the distance formula for vertical line

Since the x - coordinates of the two points \((-11,7)\) and \((-11, - 2)\) are the same (\(x_1=x_2=-11\)), the distance \(d\) between them is the absolute difference of the y - coordinates. The formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(x_1 = x_2\) is \(d=\vert y_1 - y_2\vert\).

Step2: Substitute the values of y - coordinates

Here, \(y_1 = 7\) and \(y_2=-2\). So we substitute these values into the formula: \(d=\vert7-(-2)\vert\).

Step3: Simplify the expression

First, simplify the expression inside the absolute value: \(7-(-2)=7 + 2=9\). Then, take the absolute value of 9, which is 9.

Answer:

The distance between the points \((-11,7)\) and \((-11,-2)\) is 9.