Question

One diagonal of a rhombus has endpoints (-11, -9) and (-5, -3).

Answer 1

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