What is the distance between points F(2, 9) and G(4, 14)? Round to the nearest tenth.A) ๐น๐บ =15.2B) ๐น๐บ =4.6C) ๐น๐บ =7.4D) ๐น๐บ =5.4.
Y2 - Y1 = 14 - 9 = 5
X2 - X1 = 4 - 2 = 2
hypotenuse = sqrt (25 + 4) so h^2 = 29
well h will be between 5 and 6 because 5^2 = 25 and 6^2 = 36
To find the distance between two points, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given the coordinates of point F as F(2, 9) and the coordinates of point G as G(4, 14), we can substitute the values into the formula:
Distance = sqrt((4 - 2)^2 + (14 - 9)^2)
Simplifying this expression further:
Distance = sqrt(2^2 + 5^2)
Distance = sqrt(4 + 25)
Distance = sqrt(29)
Now, let's round this to the nearest tenth.
The square root of 29 is approximately 5.4.
Therefore, the correct answer is D) ๐น๐บ = 5.4.