Question

find the distance between point ( p ) and line ( ell ).
line ( ell ) contains points ( (4,-1) ) and ( (4,9) ). point ( p ) has coordinates ( (1,6) ).
a) 3 units
b) ( sqrt{10} ) or about 3.16 units
c) ( sqrt{7} ) or about 2.65 units
d) 4 units

Explanation:

Step1: Determine the equation of line \( \ell \)

Since the \( x \)-coordinates of the two points \((4,-1)\) and \((4,9)\) on line \( \ell \) are the same (\(x = 4\)), the equation of line \( \ell \) is \(x=4\).

Step2: Calculate the distance between point \(P(1,6)\) and line \(x = 4\)

The distance \(d\) between a point \((x_0,y_0)\) and a vertical line \(x=a\) is given by \(d=\vert x_0 - a\vert\). Here, \(x_0 = 1\) and \(a = 4\), so \(d=\vert1 - 4\vert=\vert-3\vert = 3\).

Answer:

A. 3 units