what does this mean??? (math question)?

Question

IM NOT TRYING TO CHEAT BUT MATH MAKES ME CRY AND I REALL HAVE NO IDEA WHAT THE ARE TALKING ABOUT....

given ▲ABC w/ vertices A(2,2), B(6,4) and C(5,6)
a) use slope to verify that AB┴BC
b)find the permeter of ABC

Answer 1

perimeter of a shape = sum of all sides
slope intercept form : y = mx + b
where y is the y coordinate given x
m is the slope
and b is the y-intercept (value of y when x is 0)
if m is the slope of a line, another line perpendicular to the first would have a slope of -1/m (the negative inverse of m)
slope m = (final y - initial y) / (final x - initial x)

then the slope of line AB is:
(4 - 2)/(6 - 2) = (2/4) = 1/2
the slope of the line perpendicular to AB with slope m =1/2
is -1/m = -1/ (1/2) = -2
if AB┴BC then
the slope of BC should be -2
to check:
(6 - 4)/(5 - 6) = 2/-1 = -2 so AB┴BC is true

to find length of AB (2,2) (6,4),
use hypotenuse
= sqrt[(pointA y - pointB y)^2 + (pointA x - pointB x)^2]
= sqrt[(2 - 4)^2 + (2 - 6)^2]
= sqrt[(-2)^2 + (-4)^2]
= sqrt(4 + 16)
= sqrt (20)
= 2sqrt5

to find length of AC (2,2) (5,6),
use hypotenuse
= sqrt[(pointA y - pointC y)^2 + (pointA x - pointC x)^2]
= sqrt[(2 - 6)^2 + (2 - 5)^2]
= sqrt[(-4)^2 + (-3)^2]
= sqrt(16 + 9)
= sqrt (25)
= 5

to find length of BC (6,4) (5,6),
use hypotenuse
= sqrt[(pointB y - pointC y)^2 + (pointB x - pointC x)^2]
= sqrt[(4 - 6)^2 + (6 - 5)^2]
= sqrt[(-2)^2 + (1)^2]
= sqrt(4 + 1)
= sqrt5

then the perimeter is:
2sqrt5 + 5 + sqrt5
= 5 + 3sqrt5
= 11.708 units

Answer 2

a) Slope of AB is computed by taking the points A and B.
A(2, 2) and B(6, 4)
The formula to calculate the slope is m = (y2 - y1)/(x2 - x1)
In our case we will assign
y2 = 4
y1 = 2
x2 = 6
x1 = 2
Now lets plug and chug
slope (m) = (4 - 2)/(6 - 2)
= 2/4 = 1/2 is our slope (m) of line AB
Now we must find the slope of the other line BC
B(6, 4) and C(5, 6)
We will once again assign values
y2 = 6
y1 = 4
x2 = 5
x1 = 6
Using the formula again we get
slope (m) = (6 - 4)/(5 - 6)
= 2/-1 = -2 is our slope (m) of line BC
Since the slope of BC is a opposite (meaning opposite sign)recipicol (don't know if i spelled it correctly) of AB it means that the two are perpendicular (that is what the upside down T symbol means) This is one of the theorems it should be in your text book.

b) Permeter equals line AB + BC + CA
in order for us to calculate the distance of line AB, BC, and CA we have to use to distance formula. Which is
d = squareroot[(x2 - x1)^2 + (y2 - y1)^2]
So lets first find the distance of line AB
A(2, 2) and B(6, 4)
We will assign values again
y2 = 4
y1 = 2
x2 = 6
x1 = 2
Lets plug it in our formula and we get
d = squareroot[(6 - 2)^2 + (4 - 2)^2]
= squareroot[(4)^2 + (2)^2]
= squareroot[16 + 4]
= squareroot[20] this is distance of AB
Now using the same method calculate the distance of BC
B(6, 4) and C(5, 6)
assigning values again
y2 = 6
y1 = 4
x2 = 5
x1 = 6
plug and chug
d = squareroot[(5 - 6)^2 + (6 - 4)^2]
= squareroot[(-1)^2 + (2)^2]
= squareroot[1 + 4]
= squareroot[5] this is the distance of BC
Once again using the same method calculate the distance of CA
C(5, 6) and A(2, 2)
assign values
y2 = 2
y1 = 6
x2 = 2
x1 = 5
Using the distance formula we get
d = squareroot[(2 - 5)^2 + (2 - 6)^2]
= squareroot[(-3)^2 + (-4)^2]
= squareroot[9 + 16]
= squareroot[25] = 5 this is your distance from CA.
Now to calculate the premeter we add all these together
that is, AB + BC + CA
and we get
squareroot[20] + squareroot[5] + 5
approximately equals 11.7082 that is your final answer. If your teacher does not want it in decimal format then squareroot[20] + squareroot[5] + 5 is your final answer.

Email me or Im me if you need further clarification or help. Good Luck!

Answer 3

So you have a triangle, and you are trying to show that line segment AB is perpendicular to BC, and to find the perimeter of the triangle.

Well, you know the distance formula, right? It's a variant of the Pythagorean theorem. Use it to compute the distance between each pair of points, and sum all three distances to find the perimeter.

To prove that something is perpendicular, the slopes must be inverse and negative to each other. If one line segment has slope 2, the perpendicular line has slope -1/2.

Figure the slope (rise over run) for AB and BC.

Answer 4

1.) slope formula= y-y/x-x

AB slope > 2-4/2-6= -2/-4 = -1/2
BC slope > 4-6/6-5= 2/1

A segment is perpendicular to another if it is the negative reciprocol (the opposite sign and flipped upside down.)

So yes, AB is perpendicular to BC.

Answer 5

Use trigonometry to prove AB is perpendiculat to BC, and find the perimeter. Easy!!