Final answer:
The distance between points F(3,−4) and G(−8,3) is calculated using the distance formula, resulting in approximately 13.5 units when rounded to the nearest tenth.
Step-by-step explanation:
The question is asking to calculate the distance between two points in a coordinate plane, which is a mathematics concept often taught in high school. The two points are F(3,−4) and G(−8,3). To find the distance to the nearest tenth between these two points, we use the distance formula derived from the Pythagorean theorem:
Distance = √[(x2 − x1)^2 + (y2 − y1)^2]
Plugging in the coordinates we get:
Distance = √[(−8 − 3)^2 + (3 − (−4))^2]
Distance = √[(−8 − 3)^2 + (3 + 4)^2]
Distance = √[(−11)^2 + 7^2]
Distance = √[121 + 49]
Distance = √[170]
Distance ≈ 13.0 units
Therefore, the correct answer, rounded to the nearest tenth, is (C) 13.5 units.