Question

Construct a line perpendicular to m through P. Then find the distance from P to m.

Line m contains points (4.1) and (2.1). Point P has coordinates (3,5).

Answer 1

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,

`d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2`

Substituting the coordinates, we get;

`d=√((4-3)^2+(1-5)^2)`

`d=√((1)^2+(-4)^2)`

`d=√(1+16)`

`d=√(17)`

Therefore, the distance between the point P to line m is √17 units.