Answer:
(-10, -8) and (-6, -4)
Step-by-step explanation:
we know that
The diagonals of a rhombus are perpendicular
If two lines are perpendicular, then the product of their slopes is equal to -1
m1*m2=-1
step 1
Find the slope of the given diagonal
we have
(-11, -9) and (-5, -3)
m=(-3+9)/(-5+11)
m=-6/6=-1
Find the slope of the other diagonal
we have
m1=-1
Find m2
m1*m2=-1
(-1)*m2=-1
m2=1
step 2
Verify the slope of each of the endpoints of the other diagonal
The slope of the other diagonal must be equal to 1
so
case a) (-10, -4) and (-6, -8)
m=(-8+4)/(-6+10)
m=-4/4=-1
therefore
The points of case a) cannot be the end-points of the other diagonal
case b) (-8, -3) and (-5, -6)
m=(-6+3)/(-5+8)
m=-3/3=-1
therefore
The points of case b) cannot be the end-points of the other diagonal
case c) (-8, -4) and (-8, -8)
m=(-8+4)/(-8+8)
m=-4/0 -----> undefined
therefore
The points of case c) cannot be the end-points of the other diagonal
case d) (-10, -8) and (-6, -4)
m=(-4+8)/(-6+10)
m=4/4=1
therefore
The points of case d) can be the end-points of the other diagonal
