Question

A line passes through `(5 ,9 )` and `(7 ,3 )`. A second line passes through `(3 ,1 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

(4 ,-2)

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)=(5,9)" and " (x_2,y_2)=(7,3)`

`rArr m = (3-9)/(7-5) = (-6)/2 = (-3)/1 = -3`

Since the 2nd line is parallel then it's gradient equals -3

There are an infinite number of points that can lie on this line , but to find one we can use the definition of gradient and from (3 ,1) move 1 to the right and 3 down (This is equivalent to adding 1 to the x-coordinate and subtracting 3 from the y-coordinate )

hence (3 ,1) → (3+1 , 1-3) → (4 ,-2) is a point on the line.

Further points may be found in the same way.