Question

A line passes through `(2 ,3 )` and `( 4, 5 )`. A second line passes through `( 7, 8 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

(8,9)

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)=(2,3)" and " (x_2,y_2)=(4,5)`

`rArr m = (5-3)/(4-2) = 2/2 = 1`

since 2nd line is parallel to 1st , it's gradient = 1

There will be an infinite number of points that lie on the line, but to find one , using the definition of gradient

From the point (7,8) move 1 up and 1 to the right . This is equivalent to adding 1 to the y-coord and 1 to the x-coord.

hence (7,8) → (7+1,8+1) → (8,9) → (9,10) etc.