A rhombus has opposite vertices at (-1, 3) and (5, -1). Find the equations of its diagonals. One of the other vertices is (0, -2). Find the fourth vertex. Answers 2x + 3y = 7, 3x - 2y = 4; (4, 4) Solution equation of line passes throught the points (-1, 3) and (5, -1) equation of one diagonal. equation is...> (y-3)/(3-(-1))= (x-(-1))/(-1-5) (y-3)/4=(x+1)/(-6) (y-3)/2=(x+1)/-3 -3y+9=2x+2 2x+3y=7..(1)one equation of diagonal. y=(-2/3)x+7/3 two diagonals of rhombous are in perpendicular to each other. so slopes of two diagonals say (m1 and m2 ) m1*m2=-1 slope of one diagonal =m1=-2/3 -2/3*m2=-1 m2=3/2 equation of anothe digonal with the slope 3/2 and point (0,-2) y+2=(3/2)(x-0) 2y+4=3x 3x-2y=4...(2) equation of another diagonal let another vertices is (x2,y2) mid point of first diagonal=mid point anothe diagonal ((-1+5)/2 , (3-1)/2)=((x2+0)/2 ,(y2-2)/2)) (2,1)=(x2/2,(y2-2)/2) 2=x2/2 x2=4 (y2-2)/2=1 y2=2+2=4 then another vertices is (4,4).

1. A rhombus has opposite vertices at (-1, 3) and (5, -1). Find the equations of its diagonals.
One of the other vertices is (0, -2). Find the fourth vertex.
Answers
2x + 3y = 7, 3x - 2y = 4; (4, 4)
Solution
equation of line passes throught the points (-1, 3) and (5, -1) equation of one diagonal.
equation is...> (y-3)/(3-(-1))= (x-(-1))/(-1-5)
(y-3)/4=(x+1)/(-6)
(y-3)/2=(x+1)/-3
-3y+9=2x+2
2x+3y=7..(1)one equation of diagonal.
y=(-2/3)x+7/3
two diagonals of rhombous are in perpendicular to each other.
so slopes of two diagonals say (m1 and m2 )
m1*m2=-1
slope of one diagonal =m1=-2/3
-2/3*m2=-1
m2=3/2
equation of anothe digonal with the slope 3/2 and point (0,-2)
y+2=(3/2)(x-0)
2y+4=3x
3x-2y=4...(2) equation of another diagonal
let another vertices is (x2,y2)
mid point of first diagonal=mid point anothe diagonal
((-1+5)/2 , (3-1)/2)=((x2+0)/2 ,(y2-2)/2))
(2,1)=(x2/2,(y2-2)/2)
2=x2/2
x2=4
(y2-2)/2=1
y2=2+2=4
then another vertices is (4,4)