A line passes through #(9 ,2 )# and #( 3, 8 )#. 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 21, 2016
(3 , 2 )
Explanation:
The 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)=(3,8)#
#rArr m = (8-2)/(3-9) = 6/(-6) = - 1 # There are an infinite number of points that will lie on the same line as (4,1) with a gradient of -1
However , by the definition of gradient , from (4,1) , move 1 to the left and 1 up ( which means subtract 1 from x-coord and add 1 to the y-coord ) you will get a point on the line.
hence (4,1) →(4-1,1+1) → (3,2) is a point on the same line.
other points may be found in the same way.