Stuck on a Maths iGCSE Higher Tier Edexcel Question

ABCD is a rhombus. The diagonals, AC and BD, intersect at the point M. The coordinates of M are (6, -11). The points A and C both lie on the line with equation 2y+7x=20. Find the exact coordinates of the point where the line through B and D intersects the y-axis.
Any help would be much appreciated!

Hi Davros, thank you for getting back to me,
This is what I have so far:
I rearranged 2y+7x=20 to identify the gradient which is -3.5
Since they are diagonals, I believe they bisect at a perpendicular angle, so to find the gradient of BD, you would do the negative reciprocal of -3.5, so 1/3.5
Then, I used the point given as well as my calculated gradient to work out the line equation (using formula y-y1=m(x-x1)) to get y=2/7x-89/7
Since it asks for the coordinates at the y-axis, I made x=0 and solved my equation, so y=2/7(0) - 89/7 which is -89/7
So I believe the answer is (0, -89/7)
But I am not sure, because the fraction looks horrible!

Looks good. Probably better to express -89/7 as a proper fraction.
Note you could have "written down" the new equation of the line as
7y - 2x = -7*11 - 2*6 = -89
Saves having to use fractions and a bit easier to check, but your approach is more traditional and there isn't much in it.

Note it helps to post your current working/describe what you're stuck with in the original question. Saves the "what have you done so far" stock response.