Question

find the distance between point p and line l. line l contains points (-2,1) and (4,1). point p has coordinates (5,7). a) 5 units b) √35 or about 5.92 units c) √47 or about 6.96 units d) 6 units

Explanation:

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

Since the \( y \)-coordinates of the two points \((-2,1)\) and \((4,1)\) on line \( \ell \) are the same (\(y = 1\)), the equation of line \( \ell \) 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 \((x_0,y_0)\) to the line \( y = c \) is given by \( d=\vert y_0 - c\vert \).
Here, \( x_0 = 5,y_0 = 7,c = 1 \).
So \( d=\vert7 - 1\vert\).

Step3: Calculate the value

\(d=\vert7 - 1\vert=\vert6\vert = 6\)

Answer:

D. 6 units