A line passes through #(8 ,2 )# and #(2 ,1 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Mar 20, 2016

(9,6)

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)=(8,2)" and " (x_2,y_2)=(2,1) #

hence # m = (1-2)/(2-8) =(-1)/(-6) = 1/6 #

The second line is parallel and will also have # m = 1/6 #

There will be an infinite number of points along with (3,5) which will have the same gradient. To find a point (add 1 to y-coord and 6 to x-coord) From definition of gradient.

# rArr (3+6, 5+1) = (9,6) → (15,7)" is another point " #