1. P(3,1) and R(-7,5) are vertices of a rhombus PQRS. What is the equation of diagonal QS?
Write Comment
Comments
By: anil on 05 May 2019 02.18 am
Diagonals of a rhombus bisect each other perpendicularly. Thus, O is the mid point of QS and RP. Coordinates of midpoint of line joining A = $$(x_1 , y_1)$$ and B = $$(x_2 , y_2)$$ is $$(frac{x_1 + x_2}{2} , frac{y_1 + y_2}{2})$$
=> $$O = (frac{3 - 7}{2} , frac{1 + 5}{2}) = (-2 , 3)$$ Slope of PR = $$frac{1 - 5}{3 + 7} = frac{-2}{5}$$ Product of slopes of two perpendicular lines is -1 => Slope of QS = $$m imes frac{-2}{5} = -1$$ => $$m = frac{5}{2}$$ $$ herefore$$ Equation of line QS with slope $$m = frac{5}{2}$$ and passing through point O $$(x_1,y_1) = (-2,3)$$ = $$(y - y_1) = m (x - x_1)$$ = $$(y - 3) = frac{5}{2} (x + 2)$$ = $$2y - 6 = 5x + 10$$ = $$5x - 2y = -16$$
Terms And Service:We do not guarantee the accuracy of available data ..We Provide Information On Public Data.. Please consult an expert before using this data for commercial or personal use
Powered By:Omega Web Solutions
=> $$O = (frac{3 - 7}{2} , frac{1 + 5}{2}) = (-2 , 3)$$ Slope of PR = $$frac{1 - 5}{3 + 7} = frac{-2}{5}$$ Product of slopes of two perpendicular lines is -1 => Slope of QS = $$m imes frac{-2}{5} = -1$$ => $$m = frac{5}{2}$$ $$ herefore$$ Equation of line QS with slope $$m = frac{5}{2}$$ and passing through point O $$(x_1,y_1) = (-2,3)$$ = $$(y - y_1) = m (x - x_1)$$ = $$(y - 3) = frac{5}{2} (x + 2)$$ = $$2y - 6 = 5x + 10$$ = $$5x - 2y = -16$$