Calculate a if the point A(-1,2) is on the line 2x-ay+1=0

Expert Answers
hala718 eNotes educator| Certified Educator

A(-1,2)

2x - ay + 1= 0

Since the point A is on the line , then A shoulde verify the equation of the line such that:

2xA - ayA + 1 = 0

2(-1) - a(2) + 1 = 0

-2 -2a + 1 = 0

==> 2a = -1

==> a = -1/2

thewriter | Student

As the (x,y) coordinates of A are (-1,2) and it lies on the line 2x-ay+1=0, we can substitute -1 for x and 2 for y to derive the value of a.

2(-1)-a*2+1=0

=>-2-2a+1=0

=>-2a=2-1=1

=>a=-1/2

 

giorgiana1976 | Student

If a given point belongs to the line, it's coordinates verify the equation of that line.

In our case, A belongs to the given line, if and only if:

2xA - ayA + 1 = 0

We'll substitute the coordinates of A into the equation:

2*(-1) - a*2 + 1 = 0

-2 - 2a + 1 = 0

We'll combine like terms:

-2a - 1 = 0

We'll isolate -2a to the left side:

-2a = 1

We'll divide by -2:

a = -1/2

neela | Student

A point (x1,y1)  can be a point on a line ax+by+c = 0 iff  the coordinate values , if substituted in th e equation satisfies the equation. Or

ax1+by1 +c becomes zero.

Applying this to the given point A(-1,2) and the line 2x-ay+1 = 0, we get:

2(-1)-a(2)+1 = 0

-2-2a+1 = 0

-2+1 = -2a

-1 = 2a

-1/2 = 2a/2

-1/2 = a.

So a = -1/2.

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