Question

In a coordinate plane, the three vertices of rectangle OXYZ are O(0, 0), Y(b, h), and Z(b, 0), respectively. Find the vertex X.

Answer 1

In general, in the case of a rectangle, its interior angles are all right angles and two opposite sides have the same measure.

Therefore, in our case,

`\begin{gathered} OX=YZ;X=(x,y) \\ \Rightarrow√(x^2+y^2)=√((b-b)^2+h^2) \\ \Rightarrow x^2+y^2=h^2 \end{gathered}`

And

`\begin{gathered} OX\perp OZ \\ \Rightarrow(y)/(x)*(0)/(b)=-1 \\ \Rightarrow(y)/(x)\text{ is not real} \\ \Rightarrow x=0 \\ \Rightarrow y=h \end{gathered}`

Thus, the coordinates of vertex X are (0,h)