find the distance between (a,b) (-a,-b) i also need explaination
Answers
Answer:
The distance between any two points is the length of the line segment joining the points.
For example, if
A
and
B
are two points and if
¯¯¯¯¯¯¯¯
A
B
=
10
cm, it means that the distance between
A
and
B
is
10
cm.
The definition of the distance between two points is described by using a line segment of length 10 cm connecting the two points A and B.
The distance between two points is the length of the line segment joining them (but this CANNOT be the length of the curve joining them).
The definition of the distance between two points is explained using a line segment of length 7 cm and a semi-circle with circumference 22 cm.
How do we find the distance between two points if their coordinates are given?
Let's learn more about this.
Formula for Distance Between Two Points
The formula for the distance,
d
, between two points whose coordinates are
(
x
1
,
y
1
)
and
(
x
2
,
y
2
) is:
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
This is called the Distance Formula.
Let's learn how to derive this formula next.
Proof of Distance Formula
Let us assume that:
A
=
(
x
1
,
y
1
)
B
=
(
x
2
,
y
2
)
Next, we will assume that
¯¯¯¯¯¯¯¯
A
B
=
d
Now, we will plot the given points on the coordinate plane and join them by a line.
The proof of distance between two points (proof of distance formula) is shown using a coordinate plane. A line segment of length d is drawn on the graph connecting the points A(x1,y1) and B(x2,y2).
Next, we will construct a right-angled triangle with
¯¯¯¯¯¯¯¯
A
B
as the hypotenuse.
Proof of distance between two points (proof of distance formula) is shown using the coordinate plane. A right-angled triangle ABC is drawn.
Applying Pythagoras theorem for the
△
A
B
C
:
A
B
2
=
A
C
2
+
B
C
2
d
2
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
[Values from the figure]
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
[
Taking square root on both sides
]
Thus, the distance formula is proved.
now do by your self