Question

find the distance between point ( p ) and line ( ell ).
line ( ell ) contains points ( (-8,1) ) and ( (3,1) ). point ( p ) has coordinates ( (-2,4) ).
a) 3 units
b) ( sqrt{10} ) or about 3.16 units
c) ( sqrt{7} ) or about 2.65 units
d) 4 units

Explanation:

Step1: Find the equation of line \( l \)

Since the \( y - \)coordinates of the two points \((-8,1)\) and \((3,1)\) on line \( l \) are the same (\(y = 1\)), the equation of line \( l \) is \(y=1\).

Step2: Use the distance formula for a point \((x_0,y_0)\) to the line \(y = c\)

The distance \(d\) from a point \(P(x_0,y_0)=(-2,4)\) to the line \(y = c\) (here \(c = 1\)) is given by \(d=\vert y_0 - c\vert\).
Substitute \(y_0 = 4\) and \(c = 1\) into the formula: \(d=\vert4 - 1\vert\).

Answer:

A. 3 units