Question

What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?

A. 12.7 units

B. 16.9 units

C. 24.0 units

D. 33.9 units

Answer 1

What we know:
shape is rectangle which means the 2 long sides have equal distance and the 2 short sides have equal distance
we just need to find the distance of one long side and one short side for the perimeter which is the outline of the rectangle. Imagine the perimeter is the fence around the rectangle  that you would probably have to paint every 3 years and the area would be where the grass would grow in the rectangle which you would probably have to cut every weekend.

perimeter=2l+2w
 
What we need to find: PERIMETER
Using pythagorean method a² +b²=h² to find length:
From point (-6,1) to point (3,8) is a rise of 9 and a run of 9 right to get from one point to another, those are my a and b in the pythagorean formula.
a² +b²=h²
(9)²+(9)²=h²         substitution
81+81=h²            simplified
162=h²
√162=√h2           used radical properties
√162=h               length =√162

Using pythagorean method a² +b²=h² to find width:
From points (-6,-1) to point (-3,-4) is a down 3 units and left 3 units to reach from one point to another, these are my a and b for the pythagorean formula.

a² +b²=h²
(3)²+(3)²=h²
9+9=h²
18=h²
√18=√h²
√18=h           this is the width=√18

Now we find perimeter:
p=2l+2w
p=2(√162)+2(√18)
p≈33.9

D. 33.9 units

Answer 2

Using distance between two points, it is found that the perimeter of the rectangle is of 33.9 units, given by option D.

The perimeter of a rectangle of length l and width w is given by:

$P = 2(l + w)$

• In this problem, the rectangle is on the cartesian map, which means that these dimensions are found using the formula for the distance between two points.

The distance between two points $(x_0, y_0)$ and $(x_1,y_1)$ is given by:

$D = \sqrt{(x_1 - x_0)^2 + (y_1 - y_0)^2}$

The length is the distance between points (3,8) and (6,5), thus:

$l = \sqrt{(6 - 3)^2 + (5 - 8)^2} = \sqrt{18}$

The width is the distance between points (-3,-4) and (6,5), thus:

$w = \sqrt{(5 - (-4))^2 + (6 - (-3))^2} = \sqrt{162}$

Then, the perimeter is of:

$P = 2(l + w) = 2(\sqrt{18} + \sqrt{162}) = 33.9$

The perimeter is of 33.9 units, given by option D.

A similar problem is given at https://brainly.com/question/16642085