Find the slope of the line that passes through the points
1 answer:
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The distance from point A(−9,−3) to the line y = x−6 is 8.5 units
<u>What is slope ?</u>
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
step 1
Find the slope of the perpendicular line to the given line
y=x-6 ---> given line
The slope is m=1
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
m1*m2 = -1
we have
m1=1
substitute
(1)*m2 = -1
so
m2 = -1
step 2
Find the equation of the perpendicular line to the given line
The equation in point slope form is
y-y1=m(x-x1)
we have
m=-1
(x1,y1)=(−9,−3)
substitute
y+3=-1(x+9)--> equation in point slope form
y+3= -x-9
y= -x-12---> equation in slope intercept form
step 3
Find the intersection point between the given line and the perpendicular line to the given line
we have the system of equations
y = x−6.
y= -x-12
Solve the system by graphing
The intersection point is (-3,-9)
see the attached figure
step 4
we know that
The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6
the formula to calculate the distance between two points is equal to
d=√[(y2-y1)² + (x2-x1)²]
substitute the values
d=√[(-9+3)² + (-3+9)²]
d= √72 units
simplify
d= 6√2 = 8.5 units
To learn more about the slope from the given link
#SPJ1
For this questions you need to memorize formula of triangle area. for question 5, just substitute the value into the formula. for Q6 you need to use pythagorean theorem formula to find the lenght of each triangle that i already seperated
