Question

Find the perimeter of the rectangle whose vertices are the points with coordinates (-1,-9), (4-9),(-1, -3), and (4, -3).

Answer 1

Answer:

The perimeter is 22

Step-by-step explanation:

Using a graph would be the easiest way to solve this type of problem (just count the units from each point and add them all up). Perimeter= 2l+2w

If graph paper is not available then you may need to use your head a little bit and imagine a graph. You want to first find the length (or width because either can be it) by finding the two points with similar x or y values.

One of the lengths can be found by using (-1,-9) and (4,-9) because they have similar y values. Next you want to find the distance between the two values so that you can find the length. When two points are in different quadrants (use the image for reference) you would add the x values by their absolute values in meaning the distance the number is from 0 or that you change the negative numbers into positive numbers. Add 1 and 4 and you get 5. The length is 5 which you then multiply by 2 and get the length of both sides.

Because you have the two lengths the width where both of the x values are similar and find the distance between the points. You can use the two points (-1,-9) and (-1,-3). Use the absolute value of the two y values and subtract them because they are in the same quadrant (refer to the image if needed). Use the largest absolute value and subtract the lowest absolute value so that you get 9-3 which would give you 6. The width is 6 and you then multiply it by 2 so that you get 12. 12 is the width of both sides of the rectangle. Add all 4 sides together to get a perimeter of 22.

Answer 2

The perimeter of the rectangle is 10 + 2√61 units

Let the rectangle be a rectangle ABCD. For a rectangle, the measure of the opposite side are equal that is AB = CD and BC= AD

Get the measure of AB and BC using the distance formula:

$AB = \sqrt{(-9+9)^2+(4+1)^2} \\AB =\sqrt{0^2+5^2}\\AB =\sqrt{25}\\AB = 5 units$

Similarly for BC with coordinate B(4,-9) and C(-1, -3)

$BC = \sqrt{(-3+9)^2+(-4-1)^2} \\BC =\sqrt{6^2+(-5)^2}\\BC =\sqrt{36+25}\\BC =\sqrt{61} units$

Get the perimeter:

Perimeter of the rectangle =2AB + 2BC

Perimeter of the rectangle = 2(5) + 2√61

Perimeter of the rectangle = 10 + 2√61 units

Hence the perimeter of the rectangle is 10 + 2√61 units

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