Question

Determine the coordinates of the vertices of the rectangle to compute the area of the rectangle using the distance formula (round to the nearest integer).

Answer 1

34 units

Explanation:

34 units

D = dx2 + dy2 W = (5-10)2 + (10-5)2 W = (5)2 + (5)2 = 7.071 L = (5-12)2 + (10-17)2 L = (7)2 + (7)2 = 9.899 A = 2L+2W = (2)9.899+(2)7.071= 33.94 units

Answer 2

The graph of the rectangle missing in the question is shown in the figure attached.

Coordinates of the points are:

A(1,8)

B(4,5)

C(14,21)

D(17,18)

The area of the rectangle is AB*BD.

The length of a segment given two points (x1, y1) and (x2, y2) is computed as follows:

√[(y2 - y1)^2 + (x2 - x1)^2]

For segment AB:

√[(5 - 8)^2 + (4 - 1)^2] = √18

For segment BD:

√[(18 - 5)^2 + (17- 4)^2] = √338

Then, the area is:

AB*BD = (√18)*(√338) = √(18*338) = √6084 = 78