A line passes through #(2 ,6 )# and #(5 ,2 )#. A second line passes through #(3 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
1 Answer
(6 , 4)
Explanation:
The first step here is to calculate the gradient of the line passing through the 2 given points , using the
#color(blue)" gradient formula "#
#color(red)(|bar(ul(color(white)(a/a)color(black)( m = (y_2 - y_1)/(x_2 - x_1))color(white)(a/a)|)))#
where# (x_1, y_1)" and " (x_2,y_2)" are 2 points "# let
# (x_1,y_1)=(2,6)" and " (x_2,y_2)=(5,2)#
#rArr m = (2-6)/(5-2)=(-4)/3 = - 4/3 # The 2nd line is parallel and hence
# m =-4/3 " also "# There are an infinite number of points that can be on this line , but to find one, consider using the definition of the gradient.
from (3 , 8) move 4 down and 3 to the right (this is equivalent to subtracting 4 from the y-coordinate and adding 3 to the x-coordinate.)
(3 , 8) → (3+3 , 8-4) → (6 , 4)
Further points may be found in the same way.