What is the transformation of B(2 4) when dilated with a scale factor of ½ using the point (4 6) as the center of dilation?

When doing enlargements through a centre, the new position of any point is the distance of that point from the centre multiplied by the scale factor; it is easiest to treat the x- and y- coordinates separately.

To enlarge (2, 4) by a scale factor of ½ with (4, 6) as the centre of enlargement:

x: distance is (4 - 2) = 2 → new distance is 2 × ½ = 1 → new x is 2 + 1 = 3

y: distance is (6 - 4) = 2 → new distance is 2 × ½ = 1 → new y is 4 + 1 = 5

→ (2, 4) when enlarged by a scale factor of ½ with a centre of (4, 6) transforms to (3, 5).