Question

Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 2, centered at the origin where the endpoints are A(3,7) and B(4,9)

Answer 1

To perform a dilation with a scale factor of 2 centered at the origin, we need to multiply each coordinate of the original points A and B by the scale factor of 2.

The coordinates of point A after dilation are:

A′(2 * 3, 2 * 7) = A′(6, 14)

Similarly, the coordinates of point B after dilation are:

B′(2 * 4, 2 * 9) = B′(8, 18)

So, the endpoints of the dilated line segment are A′(6, 14) and B′(8, 18).

Answer 2

In a dilation centered at the origin with a scale factor of 2, each point (x,y) is transformed to a new point (2x,2y). So, to find the new coordinates of points A and B after the dilation, we simply multiply each coordinate by 2:

A = (3,7) becomes A′ = (2 * 3, 2 * 7) = (6,14)
B = (4,9) becomes B′ = (2 * 4, 2 * 9) = (8,18)

So, the new coordinates of A′ and B′ after dilation with a scale factor of 2 centered at the origin are (6,14) and (8,18), respectively