Which graphs represent functions? A.d only B. A only C. B and d D. C and d

Why is it important to calculate the distance between two points on a cartesian coordinate plane?

Gwar [14]

Answer:

Derived from the Pythagorean Theorem, the distance formula is used to find the distance between two points in the plane. The Pythagorean Theorem,

a

2

+

b

2

=

c

2

, is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuse. The relationship of sides

|

x

2

−

x

1

|

and

|

y

2

−

y

1

|

to side d is the same as that of sides a and b to side c. We use the absolute value symbol to indicate that the length is a positive number because the absolute value of any number is positive. (For example,

|

−

3

|

=

3

. ) The symbols

|

x

2

−

x

1

|

and

|

y

2

−

y

1

|

indicate that the lengths of the sides of the triangle are positive. To find the length c, take the square root of both sides of the Pythagorean Theorem.

c

2

=

a

2

+

b

2

→

c

=

√

a

2

+

b

2

It follows that the distance formula is given as

d

2

=

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

→

d

=

√

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

We do not have to use the absolute value symbols in this definition because any number squared is positive.

A GENERAL NOTE: THE DISTANCE FORMULA

Given endpoints

(

x

1

,

y

1

)

and

(

x

2

,

y

2

)

, the distance between two points is given by

d

=

√

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

Step-by-step explanation:

4 0

2 years ago

<img src="https://tex.z-dn.net/?f=the%20%5C%3A%20angle%20%5C%3A%20of%20%5C%3A%20measure%20%5C%3A%20%20%5Cfrac%7B31%5Cpi%7D%7B6%7

Yakvenalex [24]

Answer:

3rd quadrant

Step-by-step explanation:

First we just convert the angle from radians to degrees
$\frac{31\pi radians }{6}*\frac{180degrees}{\pi radians} =\frac{31*180}{6} degrees=930degrees$
Now that's too big, all this means is if we start rotating from the positive y-axis in a circle we will cross the starting point 2 times, 2 full circles;
$930degrees-360degrees=570degrees\\570degrees-360degrees=210degrees$
Now in which quadrant it 210 degrees?
0 degrees to 90 degrees is 1st quadrant
90 degrees to 180 degrees is 2nd quadrant
180 degrees to 270 degrees is 3rd quadrant
270 degrees to 360 degrees is 4th quadrant
So our answer is the 3rd quadrant.