A line passes through #(9 ,2 )# and #( 3, 5 )#. A second line passes through #( 4, 1 )#. What is one other point that the second line may pass through if it is parallel to the first line?
1 Answer
Mar 24, 2016
(6 , 0 )
Explanation:
First step is to calculate the gradient of the line passing through the 2 given points using the
#color(blue)" gradient formula " #
# m = (y_2 - y_1)/(x_2 - x_1) # where
# (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points "# let
# (x_1,y_1)=(9,2)" and (x_2,y_2)=(3,5) #
#rArr m = (5 - 2 )/(3 - 9 ) = 3/(-6) = -1/2 # Since the 2nd line is parallel then it's gradient will also be
# -1/2 # There are an infinite number of points that lie on the 2nd line.
Using the definition of gradient , to get to the next point from (4,1), move 1 down and 2 right , which is equivalent to subtracting 1 from the y-coordinate and adding 2 to the x-coord.
hence (4,1) → (4+2,1-1) → (6 , 0 )
Further points may be found in the same way- say ( 8,-1)