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completes the statement or answers the qu
COORDINATE GEOMETRY Find the distance from P to
1. Line / contains points (3,5) and (7,9). Point P has coordinates
a. 32
b.18
c. /20
d. 26

Step-by-step explanation:

The complete question is

Line L contains points (3, 5) and (7, 9). Points P has coordinates (2, 10). Find the distance from P to L

step 1

Find the equation of the line L contains points (3,5) and (7,9)

Find the slope

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

substitute the given values

Find the equation of the line in point slope form

we have

substitute

isolate the variable y

-----> equation A

step 2

Find the equation of the perpendicular line to the given line L  that passes through the point P

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal

so

The slope of the given line L  is

The slope of the line perpendicular to the given line L  is

Find the equation of the line in point slope form

we have

substitute

isolate the variable y

----> equation B

step 3

Find the intersection point equation A and equation B

-----> equation A

----> equation B

solve the system by graphing

The intersection point is (5.7)

see the attached figure

step 4

we know that

The distance from point P to the the line L is equal to the distance between the point P and point (5,7)

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

we have

(2,10) and (5,7)

substitute

simplify

see the attached figure to better understand the problem

b.my answer is b.

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