A rectangle has two opposite vertices at the points (1,2) and (5, 5). If the other vertices lie on the line x = 3, determine their co-ordinates.

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Solution

The vertices A and C are given and the vertices B and D are on the line x = 3 and hence the figure is drawn with B as (3 , $k_{1})$ and D as (3 , $k_{2})$
AC = BD $\Rightarrow$ 5 = $k_{2} - k_{1}$ ..........(1)
Diagonals bisect $\frac{k_{1} + k_{2}}{2} = \frac{7}{2}$
or $k_{2} + k_{1} = 7$ ......(2)
Solving (1) and (2) , we get $k_{1} = 1, k_{2} = 6$
$∴$ B is (3, 1) and D is (3, 6) .

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