Question

Find the length of the longest side of the rectangle whose vertices are given. A(2, 1), B(5, 4), C(0, 3), D(3, 6)

Answer 1

Draw an accurate picture of the rectangle in the x-y axis, as shown in the figure.

Clearly the longest sides are Ab and CD.

Draw point E, such that AE is perpendicular to BE.

E has the x-coordinate equal to that of B, and the y coordinate equal to that of A.

So the coordinates of E are (5, 1)

Since AE and EB are perpendicular, m(AEB)=90°.

|AE|=|EB|=3, so by the pythagorean theorem:


`|AB|= \sqrt^(2) + = \sqrt{3^(2)+ 3^(2)} = \sqrt{2*3^(2)}=3 √(2)` units


Answer:
`3√(2)` units