Find the distance OA between point A and origin O(0,0) when lines y=-2x-4 and -x+7y=17 intersect at point A

Answer 1

First, we need to find the coordinates of point A which is the point where the two lines intersect.

Given the two equations:
1) y = -2x - 4
2) -x + 7y = 17

To find the coordinates of point A, we can substitute equation 1 into equation 2:

-x + 7(-2x - 4) = 17
-x - 14x - 28 = 17
-15x - 28 = 17
-15x = 45
x = -3

Now, substitute x = -3 into equation 1 to find y:

y = -2(-3) - 4
y = 6 - 4
y = 2

So, the coordinates of point A are (-3, 2).

Now, we can find the distance OA using the distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((-3 - 0)^2 + (2 - 0)^2)
Distance = sqrt(9 + 4)
Distance = sqrt(13)

Therefore, the distance OA between point A and the origin O is sqrt(13) units.