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:
Answer:
2 and 13/60
Step-by-step explanation:
First, we must create a common denominator in the fractions. For the given denominators, it would be 60, so 3/4 would be 45/60 and 8/15 would be 32/60. From here, we can just subtract and get 2 and 13/60.
Hope this helps!
Hi! the numbers are 26 and 28!
26+(26+2) =54
Answer:
The angle is about 30.27 degrees.
Step-by-step explanation:
Use the trig ratio cosine because you are given the adjacent leg and the hypotenuse.
Plug into a calculator
Rounded to the nearest hundredth the angle is 30.27 degrees.
Answer:
The area of trapezoid is 72 cm²
Step-by-step explanation:
Given : A trapezoid with given dimensions.
We have to find the area of trapezoid ABCD.
Consider the given trapezoid ABCD ,
AB = EF = 8 cm
and CE = FD = 4 cm
Then CD = CE + EF + FD = 4 + 8 + 4 = 16 cm
Thus, Area of trapezoid = 
here, height = 6 cm
and sum of parallel sides = AB + CD = 16 + 8 = 24 cm
Thus, Area of trapezoid = 
Simplify, we have,
Area of trapezoid = 72 cm²
Thus, The area of trapezoid is 72 cm²
