Question

The circle shown below is centered at (0, 0) and passes through point P located at (2, 0). The circle is dilated with the center of dilation at the origin and a scale factor of 0.5 and then translated up 3 units. What are the coordinates of point P after this transformation?

Give your answer in correct coordinate notation without spaces: (x,y)


Give your answer in correct coordinate notation without spaces: (x,y)

Answer 1

Since the factor is 0.5, after dilated we have new circle with radius 1, so the image of P after dilatation is (1,0)

Then we move that point 3 step to up, so the last image is atin (1,3), more clear take a look for the picture

Answer 2

Based on the circle shown above, the coordinates of point P after this transformation are (1,3).

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric figure, but not its shape.

Next, we would apply a dilation centered at the origin to the coordinates of point P by using a scale factor of 0.5 as follows:

(x, y) → (0.5x', 0.5y')

P (2, 0) → (2 × 0.5, 0 × 0.5) = P' (1, 0).

Furthermore, we would apply a translation 3 units up to the new point, in order to determine the coordinates of its image as follows;

(x, y) → (x, y + 3)

P' (1, 0) → (1, 0 + 3) = P" (1, 3).