Answer:
The point that lies on the line parallel to line KL would be ( 8, - 10 )
Step-by-step explanation:
Line KL passes through the points ( - 6, 8 ) and ( 6, 0 ) while it's respective parallel line passes through point M, ( - 4, - 2 ).
Our approach here is to first determine the slope of KL such that the slope of it's parallel line will be the same, and hence we can determine a second point on this line.
Slope of KL : ( y₂ - y₁ ) / ( x₂ - x₁ ),
( 0 - 8 ) / ( 6 - ( - 6 ) ) = - 8 / 6 + 6 = - 8 / 12 = - 2 / 3
Slope of respective Parallel line : - 2 / 3,
Another point on Parallel line : ( 8, - 10 )
How can we check if this point really belongs to the parallel line? Let's take the slope given the points ( - 4, - 2 ) and ( 8, - 10 ), and check if it is - 2 / 3.
( y₂ - y₁ ) / ( x₂ - x₁ ),
( - 10 - ( - 2 ) ) / ( 8 - ( - 4 ) ) = ( - 10 + 2 ) / ( 8 + 4 ) = - 8 / 12 = - 2 / 3
And therefore we can confirm that this point belongs to line KL's parallel line, that passes through point M.
