A. What are the coordinates of the vertices of the triangle below? B. Find each side length.
C. Classify the figure. Use coordinate geometry (i. e. Pythagorean Theorem, distance formula,
slope formula, etc.) and properties of triangles to justify your response.

Solution given:

A.coordinate are

A(-2,3)

B(0,-3)

C(4,5)

B.Each length are :

we have

length

now

AB:=units

BC:=units

AC:=units

C. the figure:

By using Pythagoras law

base[b]=AB=perpendicular [p]=AC

hypotenuse [h]=BC

we have

h²=p²+b²

substituting value

()²=2p²

16*5=2*()²

80=2*4*10

80=80

SO IT IS RIGHT ANGLED ISOSCELES TRIANGLE.

Step-by-step explanation:

Solution given:

A.coordinate are

A(-2,3)

B(0,-3)

C(4,5)

B.Each length are :

we have

length \sqrt{(x2-x1)²+(y2-y1)²}

(x2−x1)²+(y2−y1)²

now

AB:\sqrt{(-2-0)²+(3+3)²}

(−2−0)²+(3+3)²

=2\sqrt{10}2

10

units

BC:\sqrt{(0-4)²+(-3-5)²}

(0−4)²+(−3−5)²

=4\sqrt{5}4

5

units

AC:\sqrt{(-2-4)²+(3-5)²}

(−2−4)²+(3−5)²

=2\sqrt{10}2

10

units

C. the figure:

By using Pythagoras law

base[b]=AB=perpendicular [p]=AC

hypotenuse [h]=BC

we have

h²=p²+b²

substituting value

(4\sqrt{5}4

5

)²=2p²

16*5=2*(2\sqrt{10}2

10

)²

80=2*4*10

80=80

SO IT IS RIGHT ANGLED ISOSCELES TRIANGLE.

step-by-step explanation:

the answer is 128

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺