Question

A line passes through `(9 ,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

One other point through which the second parallel line will pass is (2.5, 10.8)

Explanation:

Let the two lines be AB & CD.

Both the lines will have same slope ‘m’

Slope of `AB = CD = m = (5-3) / (4-9) = -(2/5)`

Equation of CD is

`y = mx + c = -(2/5)x + c`

Substituting the values of x, y of point C, we get the value of constant c

`8 = -((2/5) * 7) + c`

`c = 8+ (2/5) * 7 = 10.8`

Equation of parallel CD is

`y = -(2/5)x + 10.8`

By choosing a value for x in the above equation arbitrarily and substituting the same in this equation, we can get the. Coordinate.

Let x = (5/2), then

`y = (-5/2)(2/5)) + 10.8 = 9.8`

One other point through which the second parallel line will pass is (2.5, 10.8)