Question

The coordinates of the vertices of a rectangle are (−2,3),(4,3),(4,−4) and (−2,−4). What are the dimensions of the rectangle? A 1 unit by 2 units B 1 unit by 6 units C 7 units by 2 units D 7 units by 6 units

Answer 1

D. The dimension of the given rectangle is 7 units by 6 units.

Explanation:

Here, the given coordinates of the rectangle are as:

A(−2,3),B (4,3),C(4,−4) and D(−2,−4).

Now, as we know in a rectangle, OPPOSITES SIDES ARE EQUAL IN LENGTH

So, find the length of any two adjacent sides of the rectangle, which will give the dimensions of the rectangle.

Now, by DISTANCE FORMULA:

The distance between (a,b) and (c,d) is given as:

`√((c-a)^2+ (d-b)^2)`

So, here the distance AB with A(−2,3) ,B (4,3)

=
`√((4-(-2))^2 + (3-3)^2) = √((6)^2 +0) = 6`

or, AB = 6 units

Similarly the distance BC with B (4,3),C(4,−4)

BC =
`√((4-4)^2+(-4-3)^2) = √((-7)^2 +0) = 7`

or, BC = 7 units

Hence, the dimension of the given rectangle is 7 units by 6 units.