Diagonal of a Rhombus are perpendicular & intersects in their middle point: Assume the diagonals intersects in H
A(0,-8), B(1,-0), C(8,-4) & D(x, y) are the vertices of the rhombus and we have to calculate D(x, y)
Consider the diagonal AC. Find the coordinate (x₁, y₁) H, the middle of AC Coordinate (x₁, y₁) of H, middle of A(0,-8), C(8,-4) x₁ (0+8)/2 & y₁=(-8-4)/2 ==> H(4, -6) Now let's calculate again the coordinate of H, middle of the diagonal BD B(1,-0), D(x, y) x value = (1+x)/2 & y value=(y+0)/2 ==> x= (1+x)/2 & y=y/2 (1+x)/2 & y/2 are the coordinate of the center H, already calculated, then: H(4, -6) = [(1+x)/2 , y/2]==>(1+x)/2 =4 ==> x=7 & y/2 = -6 ==> y= -12
