Answer:
10 units
Step-by-step explanation:
Given: Point is [tex](5,9)[/tex]
To find: the distance between point [tex](5,9)[/tex] and its reflection across the y-axis
Solution:
Reflection of point [tex](x,y)[/tex] is [tex](-x,y)[/tex] across the y-axis
So, reflection of point [tex](5,9)[/tex] is [tex](-5,9)[/tex] across the y-axis
Distance between points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let [tex](x_1,y_1)=(5,9),(x_2,y_2)=(-5,9)[/tex]
So,
the distance between point (5, 9) and its reflection across the y-axis = [tex]\sqrt{(-5-5)^2+(9-9)^2}=\sqrt{100}=10[/tex]
Distance = 10 units
