perimeter of a triangle vertices L(1,5) M(-3,-3) N(3,1)?

Question

need to find the perimeter using these vertices, not sure of length of sides or how to figure them out

Answer 1

You just need to add the distances:

LM + MN + NL

The distance between two points (x1,y1) and (x2,y2) is equal to sqrt((x1-x2)^2+(y1-y2)^2) - i.e. the sqrt of the sum of the square of the differences between each coordinate - basically an application of Pythagorus Theorem.

So in this case

perimeter = sqrt(((1-(-3))^2+(5-(-3))^2) + sqrt(((-3)-3)^2+((-3)-1)^2) + sqrt((3-1)^2+(1-5)^2)

= sqrt(4^2+8^2)+sqrt((-6)^2+(-4)^2)+sqrt(2^2+(-4)^2)

= sqrt(4^2+8^2)+sqrt(6^2+4^2)+sqrt(2^2+4^2)

= sqrt(4^2(1+2^2))+sqrt(2^2(3^2+2^2))+sqrt(2^2(1+2^2))

= 4sqrt(1+4)+2sqrt(9+4)+2sqrt(1+4)

= 6sqrt(5)+2sqrt(13)

= 20.63

Don't using graphing paper uinless that is what the teacher/textbook told you to do so - there is no way it will be accurate enough.

Answer 2

in order to find the length of the sides, you need to use the distance formula three times: once, using vertices L(1, 5) and M(-3, -3) to find the distance of that side, then again w/ M and N, and then with L and N. after you find the length of each side, find the perimeter by adding the lengths all together.
here is the distance formula: sqrt [ (x1-x2)squared + (y1-y2)squared]. for example, u would find the distance between M and L like this:
sqrt [ (1-{-3})squared + (5-{-3})squared ]
sqrt [ (4)squared + (8)squared ]
sqrt [ 16 + 64 ]
sqrt [ 80] = 8.94

8.94 is the distance between M and L.
hope this helped!

Answer 3

enable A = (3,0) ...... B = (-4,2) ....... C = (-6,-5) Use distance between 2 factors formulation. AB = sqrt([-4-3]^2 + [2-0]^2) = sqrt(fifty 3) BC = sqrt([-6+4]^2 + [-5-2]^2) = sqrt(fifty 3) CA = sqrt([3+6]^2 + [0.5]^2) = sqrt(106) upload up all the climate finished perimeter = AB + BC + CA which equals = sqrt(fifty 3) + sqrt(fifty 3) + sqrt(106) which then simplifies to = 2?fifty 3 + ?106 For approximate answer, approximately 25 instruments

Answer 4

You can use the formula for the distance between 2
points (x1, y1) and (x2,y2) which is

sqrt[(x2 - x1)^2 + (y2 - y1)^2]

For example: LM = sqrt[ (-3 - 1)^2 + (-3 - 5)^2]

= sqrt(16 + 64)

= sqrt(80)

Answer 5

LM = sqrt((-3 - 1)^2 + (-3 - 5)^2)
LM = sqrt((-4)^2 + (-8)^2)
LM = sqrt(16 + 64)
LM = sqrt(80)

MN = sqrt((3 - (-3))^2 + (1 - (-3))^2)
MN = sqrt((3 + 3)^2 + (1 + 3)^2)
MN = sqrt(6^2 + 4^2)
MN = sqrt(36 + 16)
MN = sqrt(52)

LN = sqrt((3 - 1)^2 + (1 - 5)^2)
LN = sqrt(2^2 + (-4)^2)
LN = sqrt(4 + 16)
LN = sqrt(20)

LM + MN + LN = sqrt(80) + sqrt(52) + sqrt(20) = 4sqrt(5) + 2sqrt(13) + 2sqrt(5) = 6sqrt(5) + 2sqrt(13) = about 20.6275

ANS : about 20.63

Answer 6

sketch it on graph paper and draw right triangles to find the length of all 3 sides