SOLUTION: how would you find the perimeter and area of a shape with the coordinates (-3,4), (1,5), (2,1), and (-2,0)? HELP ME PLEEAASEEE!!!!!!

Algebra ->  Length-and-distance -> SOLUTION: how would you find the perimeter and area of a shape with the coordinates (-3,4), (1,5), (2,1), and (-2,0)? HELP ME PLEEAASEEE!!!!!!      Log On


   

Question 926884: how would you find the perimeter and area of a shape with the coordinates (-3,4), (1,5), (2,1), and (-2,0)?
HELP ME PLEEAASEEE!!!!!!
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
(-3,4),
(1,5), D = sqrt%281+%2B16%29
(2,1), D = sqrt%2816+%2B+1%29
(-2,0) D = sqrt%281+%2B+16%29
square: s = √17
P = 4√17
A = 17 units^2

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

plot points:

find the distance:
Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (-2, 0), we can say (x1, y1) = (-2, 0)
So x%5B1%5D+=+-2, y%5B1%5D+=+0


Since the second point is (-3, 4), we can also say (x2, y2) = (-3, 4)
So x%5B2%5D+=+-3, y%5B2%5D+=+4


Put this all together to get: x%5B1%5D+=+-2, y%5B1%5D+=+0, x%5B2%5D+=+-3, and y%5B2%5D+=+4

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (-2, 0) and (-3, 4)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%28-2+-+%28-3%29%29%5E2+%2B+%280+-+4%29%5E2%29 Plug in x%5B1%5D+=+-2, y%5B1%5D+=+0, x%5B2%5D+=+-3, and y%5B2%5D+=+4


d+=+sqrt%28%28-2+%2B+3%29%5E2+%2B+%280+-+4%29%5E2%29


d+=+sqrt%28%281%29%5E2+%2B+%28-4%29%5E2%29


d+=+sqrt%281+%2B+16%29


d+=+sqrt%2817%29


d+=+4.12310562561766

==========================================================

Answer:


The distance between the two points (-2, 0) and (-3, 4) is exactly sqrt%2817%29 units


The approximate distance between the two points is about 4.12310562561766 units



So again,


Exact Distance: sqrt%2817%29 units


Approximate Distance: 4.12310562561766 units





Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (1, 5), we can say (x1, y1) = (1, 5)
So x%5B1%5D+=+1, y%5B1%5D+=+5


Since the second point is (-3, 4), we can also say (x2, y2) = (-3, 4)
So x%5B2%5D+=+-3, y%5B2%5D+=+4


Put this all together to get: x%5B1%5D+=+1, y%5B1%5D+=+5, x%5B2%5D+=+-3, and y%5B2%5D+=+4

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (1, 5) and (-3, 4)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%281+-+%28-3%29%29%5E2+%2B+%285+-+4%29%5E2%29 Plug in x%5B1%5D+=+1, y%5B1%5D+=+5, x%5B2%5D+=+-3, and y%5B2%5D+=+4


d+=+sqrt%28%281+%2B+3%29%5E2+%2B+%285+-+4%29%5E2%29


d+=+sqrt%28%284%29%5E2+%2B+%281%29%5E2%29


d+=+sqrt%2816+%2B+1%29


d+=+sqrt%2817%29


d+=+4.12310562561766

==========================================================

Answer:


The distance between the two points (1, 5) and (-3, 4) is exactly sqrt%2817%29 units


The approximate distance between the two points is about 4.12310562561766 units



So again,


Exact Distance: sqrt%2817%29 units


Approximate Distance: 4.12310562561766 units





Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (1, 5), we can say (x1, y1) = (1, 5)
So x%5B1%5D+=+1, y%5B1%5D+=+5


Since the second point is (2, 1), we can also say (x2, y2) = (2, 1)
So x%5B2%5D+=+2, y%5B2%5D+=+1


Put this all together to get: x%5B1%5D+=+1, y%5B1%5D+=+5, x%5B2%5D+=+2, and y%5B2%5D+=+1

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (1, 5) and (2, 1)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%281+-+2%29%5E2+%2B+%285+-+1%29%5E2%29 Plug in x%5B1%5D+=+1, y%5B1%5D+=+5, x%5B2%5D+=+2, and y%5B2%5D+=+1


d+=+sqrt%28%28-1%29%5E2+%2B+%284%29%5E2%29


d+=+sqrt%281+%2B+16%29


d+=+sqrt%2817%29


d+=+4.12310562561766

==========================================================

Answer:


The distance between the two points (1, 5) and (2, 1) is exactly sqrt%2817%29 units


The approximate distance between the two points is about 4.12310562561766 units



So again,


Exact Distance: sqrt%2817%29 units


Approximate Distance: 4.12310562561766 units




Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (-2, 0), we can say (x1, y1) = (-2, 0)
So x%5B1%5D+=+-2, y%5B1%5D+=+0


Since the second point is (2, 1), we can also say (x2, y2) = (2, 1)
So x%5B2%5D+=+2, y%5B2%5D+=+1


Put this all together to get: x%5B1%5D+=+-2, y%5B1%5D+=+0, x%5B2%5D+=+2, and y%5B2%5D+=+1

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (-2, 0) and (2, 1)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%28-2+-+2%29%5E2+%2B+%280+-+1%29%5E2%29 Plug in x%5B1%5D+=+-2, y%5B1%5D+=+0, x%5B2%5D+=+2, and y%5B2%5D+=+1


d+=+sqrt%28%28-4%29%5E2+%2B+%28-1%29%5E2%29


d+=+sqrt%2816+%2B+1%29


d+=+sqrt%2817%29


d+=+4.12310562561766

==========================================================

Answer:


The distance between the two points (-2, 0) and (2, 1) is exactly sqrt%2817%29 units


The approximate distance between the two points is about 4.12310562561766 units



So again,


Exact Distance: sqrt%2817%29 units


Approximate Distance: 4.12310562561766 units




since all same, means you have a square;
so, the perimeter will be P=4d=4%284.123%29=16.492
and area A=d%5E2=%284.123%29%5E2=16.999