Question

A line passes through `(2 ,6 )` and `(5 ,2 )`. A second line passes through `(3 ,8 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

(6 , 4)

Explanation:

The first step here is to calculate the gradient of the line passing through the 2 given points , using the `color(blue)" gradient formula "`

`color(red)(|bar(ul(color(white)(a/a)color(black)( m = (y_2 - y_1)/(x_2 - x_1))color(white)(a/a)|)))`
where `(x_1, y_1)" and " (x_2,y_2)" are 2 points "`

let `(x_1,y_1)=(2,6)" and " (x_2,y_2)=(5,2)`

`rArr m = (2-6)/(5-2)=(-4)/3 = - 4/3`

The 2nd line is parallel and hence `m =-4/3 " also "`

There are an infinite number of points that can be on this line , but to find one, consider using the definition of the gradient.

from (3 , 8) move 4 down and 3 to the right (this is equivalent to subtracting 4 from the y-coordinate and adding 3 to the x-coordinate.)

(3 , 8) → (3+3 , 8-4) → (6 , 4)

Further points may be found in the same way.