Answer:
(8,-10)
Step-by-step explanation:
step 1
Find the slope of line KL
K(-6,8),L(6,0)
m=(0-8)/(6+6)
m=-8/12=-2/3
step 2
Find the slope of the line that is parallel to KL
we know that
If two lines are parallel , then their slopes are the same
therefore
The slope of the parallel line to KL is m=-2/3
step 3
Find the equation of the line parallel to KL that pass through the point M
M(-4,-2)
The equation of the line into point slope form is equal to
y-y1=m(x-x1)
substitute
y+2=-(2/3)(x+4)
step 4
Verify the points
we know that
If the point lie on the line, then the point must satisfy the equation of the line
case a) (-10,0)
substitute the value of x and the value of y in the equation and then compare the result
-10+2=-(2/3)(0+4)
-8=-8/3 -----> is not true
therefore
The point is not on the line
case b) (-6,2)
substitute the value of x and the value of y in the equation and then compare the result
2+2=-(2/3)(-6+4)
4=4/3 -----> is not true
therefore
The point is not on the line
case c) (0,-6)
substitute the value of x and the value of y in the equation and then compare the result
-6+2=-(2/3)(0+4)
-4=-8/3 -----> is not true
therefore
The point is not on the line
case d) (8,-10)
substitute the value of x and the value of y in the equation and then compare the result
-10+2=-(2/3)(8+4)
-8=-8 -----> is true
therefore
The point is on the line
