Can you please explain how I would solve these questions?

1) Which point is 2 units from the line 12x-9y-5=0?
a)(8,3)
b)(7/6, -7/3)
c)(14,6)
d)(1,1)

2.) Which of the following sets of vectors spans R2:
a) {(1,1),(-2,-2)}
b) {(1,1),(1,2)}
c) {(1,2),(1/2,2)}
d) {(-1,1),(1,-1)}

1 answer

For any point (a,b)

|12a - 9b - 5| /√(144+81) = 2
12a - 9b - 5 = 30
12a - 9b = 35

Now test which ordered pair satisfies this linear equation.