Question

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?

Answer 1

(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)