Find the distance OA between point A and origin (0,0) when lines y=x+4 and x +2y=11 intersect at point A

Answer 1

To find the point of intersection A between the two lines, we need to solve the system of equations:

y = x + 4
x + 2y = 11

Substitute y from the first equation into the second equation:

x + 2(x + 4) = 11
x + 2x + 8 = 11
3x = 3
x = 1

Now substitute x back into the first equation to find y:

y = 1 + 4
y = 5

So the point of intersection A is (1, 5).

To find the distance OA between point A and the origin (0, 0), we can use the distance formula:

OA = √((x2 - x1)^2 + (y2 - y1)^2)
OA = √((1 - 0)^2 + (5 - 0)^2)
OA = √(1 + 25)
OA = √26

Therefore, the distance OA between point A and the origin is √26 units.