To find the distance between points L(-3,-4) and T(5,5), you can use the distance formula, which is based on the Pythagorean theorem in a Cartesian plane. The distance formula is:
�
=
(
�
2
−
�
1
)
2
+
(
�
2
−
�
1
)
2
d=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
where (x₁, y₁) = (-3, -4) and (x₂, y₂) = (5, 5).
Plug these values into the formula:
�
=
(
5
−
(
−
3
)
)
2
+
(
5
−
(
−
4
)
)
2
d=
(5−(−3))
2
+(5−(−4))
2
Simplify inside the square root:
�
=
(
5
+
3
)
2
+
(
5
+
4
)
2
d=
(5+3)
2
+(5+4)
2
�
=
(
8
2
+
9
2
)
d=
(8
2
+9
2
)
�
=
(
64
+
81
)
d=
(64+81)
�
=
145
d=
145
Now, round the square root of 145 to the nearest whole number:
�
≈
145
≈
12.04
d≈
145
≈12.04
So, the distance between points L and T to the nearest whole number is approximately 12.