Final answer:
The distance between points A(-4,5) and B(6,-2) is found using the distance formula derived from the Pythagorean theorem. By applying the formula, the distance is calculated to be approximately 12.2 units to the nearest tenth.
Step-by-step explanation:
The student has asked to find the distance between two points A(-4,5) and B(6,-2) to the nearest tenth. To calculate the distance between two points (A and B) in the Cartesian plane, we use the distance formula which is derived from the Pythagorean theorem.
The distance formula is:
d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)
In this case, the coordinates are:
- A(-4,5) where x_1 = -4 and y_1 = 5
- B(6,-2) where x_2 = 6 and y_2 = -2
Plugging these values into the distance formula, we get:
d = √((6 - (-4))^2 + (-2 - 5)^2)
d = √((6 + 4)^2 + (-7)^2)
d = √(10^2 + 49)
d = √(100 + 49)
d = √149
d ≈ 12.2
Therefore, the distance between points A and B to the nearest tenth is 12.2 units.