Find the distance OA between point A and origin O (0,0) when lines y=3x-2 and 3x+2y=14 intersect at point A
To find point A where the two lines intersect, we can set the equations of the lines equal to each other:
3x - 2 = y
3x + 2y = 14
Substitute the value of y from the first equation into the second equation:
3x + 2(3x - 2) = 14
3x + 6x - 4 = 14
9x - 4 = 14
9x = 18
x = 2
Now, substitute the value of x back into the first equation to find y:
y = 3(2) - 2
y = 6 - 2
y = 4
So, point A is (2, 4).
To find the distance OA between point A and the origin O (0, 0), we can use the distance formula:
OA = sqrt((x2 - x1)^2 + (y2 - y1)^2)
OA = sqrt((2 - 0)^2 + (4 - 0)^2)
OA = sqrt(4 + 16)
OA = sqrt(20)
OA = 2sqrt(5)
Therefore, the distance OA between point A and the origin O is 2sqrt(5) units.