Answer:
The distance is
Step-by-step explanation:
step 1
Find the slope of the give line
we have
y=x+2
so
the slope m is equal to
m=1
step 2
Find the slope of the perpendicular line to the given line
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal of each other
so
we have
m=1 -----> slope of the given line
therefore
The slope of the perpendicular line is equal to
m=-1
step 3
With m=-1 and the point (8,4) find the equation of the line
y-y1=m(x-x1)
substitute
y-4=-(x-8)
y=-x+8+4
y=-x+12
step 4
Find the intersection point lines y=x+2 and y=-x+12
y=x+2 -----> equation A
y=-x+12 ----> equation B
Adds equation A and equation B
y+y=2+12
2y=14
y=7
Find the value of x
y=x+2 -----> 7=x+2 -----> x=5
The intersection point is (5,7)
step 5
Find the distance between the point (8,4) and (5,7)
we know that
The distance from the point (8,4) to the line y=x+2 is equal to the distance from the point (8,4) to the point (5,7)
Find the distance AB
the formula to calculate the distance between two points is equal to
substitute
see the attached figure to better understand the problem
