To find the distance [tex]\( XY \)[/tex] between two points [tex]\( X \)[/tex] and [tex]\( Y \)[/tex] in a plane, we use the Euclidean distance formula. The formula for the distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Given the coordinates:
[tex]\( X = (8, 4) \)[/tex]
[tex]\( Y = (-8, 0) \)[/tex]
First, we identify the values of [tex]\( x_1, y_1, x_2, \)[/tex] and [tex]\( y_2 \)[/tex]:
- [tex]\( x_1 = 8 \)[/tex]
- [tex]\( y_1 = 4 \)[/tex]
- [tex]\( x_2 = -8 \)[/tex]
- [tex]\( y_2 = 0 \)[/tex]
Next, we plug these values into the distance formula:
[tex]\[ d = \sqrt{((-8) - 8)^2 + (0 - 4)^2} \][/tex]
[tex]\[ d = \sqrt{(-8 - 8)^2 + (0 - 4)^2} \][/tex]
[tex]\[ d = \sqrt{(-16)^2 + (-4)^2} \][/tex]
[tex]\[ d = \sqrt{256 + 16} \][/tex]
[tex]\[ d = \sqrt{272} \][/tex]
On calculation, we get:
[tex]\[ d \approx 16.492422502470642 \][/tex]
Thus, the distance [tex]\( XY \)[/tex] is approximately 16.49. So, the correct answer is:
A. 16.49
