Question

pqrs is a rhombus such that pr and qs intersect at origin and pr is 8 units and qs is 6 units.find the points of the vertices lie on the plane if p is (0,4)

Answer 1

(-3 , 0) , (0 , - 4) , ( 3 , 0)  are the points of the vertices of pqrs rhombus

Step-by-step explanation:

pqrs is a rhombus such that pr and qs intersect at origin

Let say origin is o

pr = 8 unit

=> op = or = pr/2 = 8/2 = 4 units

o = (0,0)

p = (0, 4)

r = (x , y)

0 = (0 + x)/2 , 0 = (4 + y)/2

=> x = 0  y = -4

r = (0 , - 4)

pr lies on y axis

=> qs would be parallel to x axis  ( as rhombus  diagonal perpendicularrly bisect each other )

qs passes though (0, 0)

so it lies on x axis

qs = 6 units

oq = os = qs/2 = 6/2 = 3 units

q & s  would be

(-3 , 0) & ( 3 , 0)

(-3 , 0) , (0 , - 4) , ( 3 , 0)  are the points of the vertices

Learn more:

Vertex A (4, –5) and point of intersection O (–6, 7) of diagonals of ...

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Answer 2

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