Question

The endpoints of one diagonal of a rhombus are (0, -8) and (8, -4). If the coordinates of the 3rd vertex are (1, 0), what are the coordinates of the 4th vertex?
(7, -12)
(7, -8)
(-8, -4)
(-4, -12)

Answer 1

Answer:

The fourth coordinate of rhombus is (7,-12)

A is correct.

Step-by-step explanation:

The endpoints of one diagonal of a rhombus are (0, -8) and (8, -4).

If the coordinates of the 3rd vertex are (1, 0)

Let 4th vertex be (a,b)

The diagonal of the rhombus is perpendicular bisector each other.

Mid of point of both diagonal must be same.

Mid-point formula:

$(x,y)\rightarrow (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Mid-point of  (0, -8) and (8, -4)

Mid-point: $(\frac{0+8}{2},\frac{-8-4}{2})\rightarrow (4,-6)$

Mid-point of (1,0) and (a,b)

Mid-point:  $(\frac{1+a}{2},\frac{0+b}{2})\rightarrow (4,-6)$

1+a=8          and           b=-12

a=7  and  b=-12

Hence, The fourth coordinate of rhombus is (7,-12)

Answer 2

The answer is (-7, -12).

Attached is the graph to show the answer.