Given:
A line is constructed perpendicular to m through P.
Line m contains points (4,1) and (2,1)
The point P has coordinates (3,5)
We need to determine the distance from P to m.
Distance from P to m:
Let us find the distance between the point P(3,5) and the coordinate of line m (4,1)
The distance between the two point can be determined using the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Substituting the coordinates, we get;
[tex]d=\sqrt{(4-3)^2+(1-5)^2}[/tex]
[tex]d=\sqrt{(1)^2+(-4)^2}[/tex]
[tex]d=\sqrt{1+16}[/tex]
[tex]d=\sqrt{17}[/tex]
Therefore, the distance between the point P to line m is √17 units.
