Question

A line passes through `(3 ,6 )` and `(4 ,5 )`. A second line passes through `(7 ,3 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

`color(violet)("One other point on the second line is " (5,5)`

Explanation:

`"Slope of line 1 " = m = (y_2 - y_1) / (x_2 - x_1) = (5-6) / (4-3) = -1`

![https://www.askiitians.com/iit-jee-straight-line/distance-between-two-parallel-lines/]()

As `2^(nd)` line is parallel to the first line, slope of second line also `-1`

#"Equation of second line in point - slope form is "

`(y - 3) = -1 * (x - 7)`

`x + y = 10`

Let y = 5. Then x = 5#

graph{-x + 10 [-10, 10, -5, 5]}

`color(violet)("One other point on the second line is " (5,5)`