A rectangle has two opposite vertices at the points (1, 2) and (5, 5). If the other vertices lie on the line $x = 3$, , the coordinates of the vertex nearer the axis of $x$ are 

Let the coordinates of the other vertices lying on $x = 3$ be $\left(3,y_1\right)\text{ and }\left(3,y_2\right)$

Since the diagonals of a rectangle are equal and bisect each other, we have

$\frac{y_1+y_2}{2}=\frac{5+2}{2}\Rightarrow y_1+y_2=7$

and $\left|y_2-y_1\right|=\sqrt{(5-1{)}^2+(5-2{)}^2}=\sqrt{16+9}=5$

If $y_2>y_1\text{ then }{y}_2=6,y_1=1$

So that the coordinates of the vertex nearer the axis of $x$ are (3, 1)