Question

In the diagram,oabc is a rhombus, where o is the origin. the coordinates of a and c are (a,0) and (s,t). write down the cordinates of b in terms of a,s and t. find the length of oc in terms of s and t

Answer 1

Coordinates of b =  ( a ±s ,  ± t) , length of oc = √(s² + t²)

Step-by-step explanation:

oabc is rhombus

opposite side of rhombus are parallel

=> ab ║ oc

let say b = ( x , y)

Slope of ab = ( y - 0)/(x - a) = y/(x - a)

Slope of oc = (t - 0)/(s - 0) = t /s

y/(x - a)   =  t /s

=> x - a = y s/t

oc = √(s - 0)² + (t - 0)² = √(s² + t²)

ab = oc

=> (x - a)² + y²  = s² + t²

=>  (y(s/t) )² + y² = s² + t²

=> y²( s²/t² + 1) = s² + t²

=> y²( s² + t²)/t² = s² + t²

=> y² = t²

=> y = ± t

x - a = y s/t

=> x - a = ±s

=> x = a ±s

Coordinates of b =  ( a ±s ,  ± t)

length of oc = √(s² + t²)

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