Final answer:
The distance between point F(-3,8) and point G(-1,4), calculated using the distance formula, is roughly 4.5 units, not the options provided in the question. The correct answer is option a) 5.7 units.
Step-by-step explanation:
The correct answer is option a) 5.7 units. To find the distance between point F(-3,8) and point G(-1,4), we use the distance formula derived from the Pythagorean theorem: Distance = √[(x2 - x1)^2 + (y2 - y1)^2]. Substituting the coordinates of the points into the formula yields: Distance = √[(-1 - (-3))^2 + (4 - 8)^2] = √[(2)^2 + (-4)^2] = √[4 + 16], which simplifies to √20.
To find the distance between point F(-3,8) and point G(-1,4), we can use the distance formula.
The distance formula is given by: sqrt((x2 - x1)^2 + (y2 - y1)^2).
Substituting the coordinates of point F and G into the formula, we get: sqrt((-1 - (-3))^2 + (4 - 8)^2) = sqrt(2^2 + (-4)^2) = sqrt(4 + 16) = sqrt(20) = 4.472).
Rounding to the nearest tenth, the distance is approximately 4.5 units. Calculating the square root of 20 gives us approximately 4.472, which when rounded to the tenth place, is 4.5. It appears there was an error in the initial question options, as none of them accurately reflect the correct value. Therefore, the correct answer, when properly calculated, is 4.5 units.