Find the perimeter of the triangle with the vertices at (1, 2), (-5, 6), and (-3, -5).?

Answer 1

26.4536. I could be wrong. Someone pls check.

Answer 2

First, draw the picture. It always helps!
Next, use the distance formula to find the distance between each of the points.
finally, add them up.
The distance formula is based on the pythagorean relationship, that in a right triangle, c^2 = a^2 + b^2, where 2 is the hypotenuse, and a and b are the legs. The legs are the differences between the x coodrinates, and the differences between the y cooridnates. This may all seem too complicated but if you draw the picture yourself, carefully, by hand, on graph paper, you'll see. There is no substitute for understanding!
Ok, here we go ...
the distance between (1,2) and (-5,6) would be
sqrt ((1-(-5))^2 + (2-6)^2) = sqrt (6^2 + 4^2) = sqrt (52) = 2 sqrt 13.
The distance between (1,2) and (-3,-5) would be
sqrt ((1-(-3))^2 + (2 -(-5))^2 ) = sqrt (4^2 + 7^2) = sqrt (65) = sqrt (5) * sqrt (13). The reason I'm factoring out the square roots is so that I can add them in exact form. I don't like decimal approximations and I avoid then whenever possible. Finallly, the distance between (-3, -5) and (-5, 6) would be
sqrt ((-3 - (-5))^2 + (-5 - 6)^2) = sqrt (4 + 121) = sqrt (125) = 5 sqrt 5. So you have 2 sqrt 13 + sqrt 65 + 5 sqrt 5. Looks like there's no nice way to combine these algebraically so you may as well pull out the calculator for a decimal approximation if this is needed. that would be approx 26.453. Otherwise I'd leave it just like this.
Now try it yourself!

Answer 3

Using the distance formula

(1,2) and (-5,6)
D = sqrt((-5 - 1)^2 + (6 - 2)^2)
D = sqrt((-5 + (-1))^2 + 4^2)
D = sqrt((-6)^2 + 16)
D = sqrt(36 + 16)
D = sqrt(52)
D = 2sqrt(13)

(-5,6) and (-3,-5)
D = sqrt((-3 - (-5))^2 + (-5 - 6)^2)
D = sqrt(2^2 + (-5 + (-6))^2)
D = sqrt(4 + (-11)^2)
D = sqrt(4 + 121)
D = sqrt(125)
D = 5sqrt(5)

(1,2) and (-3,-5)
D = sqrt((-3 - 1)^2 + (-5 - 2)^2)
D = sqrt((-3 + (-1))^2 + (-5 + (-2))^2)
D = sqrt((-4)^2 + (-7)^2)
D = sqrt(16 + 49)
D = sqrt(65)

P = a + b + c

P = sqrt(65) + 5sqrt(5) + 2sqrt(13)
P = about 26.45

ANS : about 26.45

Answer 4

here's the equation:
1. label the points, 1, 2, and 3
2. do: (y2-y1)/(x2-x1) [the y-value of point 2 - the y-value of point one, OVER the x-value of point 2 - the x-value of point 1] do this to link all three points
so like:
point1 = (1,2)
point2= (-5, 6)
(6-2)/(-5-1) = (4)/(-6) = -2/3. do this for all three sides and add up the lengths to get the perimeter

Answer 5

using the distance formuls
side 1=rt[4^2+(-6)^2]=2rt13
side 2=rt[(-11)^2+2^2]=5rt5
side 3=rt[(-7)^2+(-4)^2]=rt65
perimeter=7.21+11.18+8.06
=26.45 units

Answer 6

It looks like someone's trying to cheat on their homework!!!!