Line l contains the points (1,5) and (4, -4). point p has the coordinates (-1, 1)
find the distance from p to l

The distance from p to l is

Step-by-step explanation:

we know that

The distance between point p from line l is equal to the perpendicular segment from line l to point p

step 1

Find the slope of line l

we have the points

(1,5) and (4, -4)

The formula to calculate the slope between two points is equal to

substitute the values

step 2

Find the equation of the line l

The equation in point slope form is equal to

we have

substitute

-----> equation A

step 3

Find the slope of the line perpendicular to the line l

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (The product of their slopes is equal to -1)

we have

---> slope of line l

therefore

----> slope of the line perpendicular to line l

step 4

Find the equation of the line perpendicular to line l that passes through the point p

The equation in point slope form is equal to

we have

substitute

-----> equation B

step 5

Solve the system of equations

-----> equation A

-----> equation B

Solve the system by graphing

The solution of the system is the intersection point both graphs

The solution is the point q(2,2)

see the attached figure

step 6

we know that

The distance between the point p and the line l is equal to the distance between the point p and the point q

the formula to calculate the distance between two points is equal to

we have the points

p(-1,1) and q(2,2)

substitute the values

step-by-step explanation:

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step-by-step explanation: this is a answer