Question

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

Answer 1

1), Coordinates of B are [(a + s), t].

2). Length of OC = $\sqrt{s^{2}+t^{2}}$

Step-by-step explanation:

Since OABC is a rhombus, where O is the origin and coordinates of C and A are (s, t) and (a, 0).

(1), Coordinates of B will be [(a + s), t]

[ By the properties of a rhombus, horizontal distance of point C is equal to the horizontal distance of B from point A.

So x-coordinates of point B = (a + s)

And vertical distance from x-axis of point B is same as point C]

(2)Length of OC = Distance between the origin and point C(s, t)

OC = $\sqrt{(x-x')^{2}+(y-y')^{2}}$

      = $\sqrt{(s-0)^{2}+(t-0)^{2}}$

OC = $\sqrt{s^{2}+t^{2}}$

Learn more about the rhombus from https://brainly.in/question/2863733