Question

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?

Answer 1

(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 "`