Question

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?

Answer 1

(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.