Answer:
The distance between the two points is 5
√
2
Explanation:
Using the distance formula,
⇒
d
=
√
(
x
1
−
x
2
)
^2
+
(
y
1
−
y
2
)
^2
we can plug in our points,
⇒
P
1=
(
−
4
,
6
)
⇒
P
2
=
(
3
,
7
)
and solve for the distance:
⇒
d
=
√
(
x
1
−
x
2
)
^2+
(
y
1
−
y
2
)
^2
⇒
d
=
√(
(
−
4
−
3
)^
2
+
(
6
−
7
)
^2)
⇒
d
=
√
((
−
7
)
^2
+
(
−
1
)^
2)
⇒
d
=
√(
49
+
1)
⇒
d
=
√
50
⇒
d
=
√(
25
⋅
2)
⇒
d
=
√(
5^
2 ⋅ 2)
⇒
d
=
√
5
^2 ⋅ √
2
⇒
d
=
5 ⋅ √
2
⇒
d
=
5
√
2
