The diagonals of a rhombus are perpendicular bisectors of each other, so we can set up the following system of equations:
(-y-5) + (-27+8) = 0
(-10x-8) + 989 = 0
Solving for y and x, we get:
y = -10
x = -99.7
Since the diagonals of a rhombus bisect each other, we know that the length of each diagonal is half the length of the other diagonal. Let's call the length of the shorter diagonal z. Then we have:
z^2 = (-y-5)^2 + (-27+8)^2
z^2 = (-10)^2 + (19)^2
z^2 = 401
z = sqrt(401) = 20.03
So the value of z is approximately 20.03. hopper this helped i’m pretty sure that’s correct