Question

24. In the diagram, OABC is a rhombus, where
is the origin, The coordinates of
A and Care (a,0) and (s, t) respectively.
C
(s. 1)
O
a
A (a.0)
() Write down the coordinates of B in terms of a, s and t.
(11) Find the length of OC in terms of s and .​

Answer 1

The coordinates of B in terms of a, s and t and the length of OC in terms of s and t -

• Extend BC to meet the y-axis at M and CP parallel to OM meet x-axis at P
• Let BQ meet x-axis at Q such that BQ is parallel to OM.
• Length of OM=CP=BQ =t
• CM= s
• In right ΔOCM, OM²+CM²=OC²
• Putting the values, t²+s²=OC²
• Therefore, OC = √t²+s²
• In ΔBQA, BQ² + QA² = AB²
• t² + QA² = t²+s² (OC=AB)
• QA=s
• Therefore, coordinates of B = (a+s, t)