Write the equition of the line that passes through the pair of points (8,-8) and (9,-4)
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Answer:
Step-by-step explanation:
<u><em>The complete question is</em></u>
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)
<em>Find the slope</em>
The formula to calculate the slope between two points is equal to
substitute the given values
<em>Find the equation of the line in point slope form</em>
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
<em>Find the equation of the line in point slope form</em>
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
