Question

Given that the points (-1,6). (3,6), (3, 1), and (-1, 1) are vertices of a rectangle, how much shorter is the width than the length?

Answer 1

Since the given coordinates are already in order,
then and two consecutive distances between the coordinates will give length and breadth,

Using distance formula,
$\sqrt{ {( - 1 - 3)}^{2} + {(6 - 6)}^{2} } \\ = \sqrt{ { (- 4)}^{2} } \\ = \sqrt{16 } \\ = 4$
(we'll not consider the negative value since distances can't be negative)

Applying this again on 2nd and 3rd coordinates,
$\sqrt{ {(3 - 3)}^{2} + {(6 - 1)}^{2} } \\ = \sqrt{ {5}^{2} } \\ = 5$
(we'll not consider the negative value since distances can't be negative)

Since length's always gotta be greater than bredth
therefore,
the difference will be 5-4= 1 units


Hence width is 1 unit shorter than length.



Note: Unit used is "unit/s"