Question

Quardrilateral DEFG is dilated by a factor of 0.5 with the center (0,0) what are the new coordinates of point D?

Answer 1

The new coordinates of point D after the dilation by a factor of 0.5 with the center at (0,0) are (0,0).

Step-by-step explanation:

When a figure is dilated by a scale factor of 0.5 with the center of dilation at the origin (0,0), each point in the original figure moves half the distance towards the origin.

As point D is likely located at the origin or at (0,0), after a dilation with the center at (0,0) by a factor of 0.5, the point remains unchanged at (0,0). This occurs because any point on the coordinate plane, when dilated about the origin by a factor of 0.5, maintains its position if it lies on the origin itself.

Answer 2

The new coordinates of point D after dilating quadrilateral DEFG by a factor of 0.5 with the center (0,0) are
`(x_D', y_D') = (0.5x_D, 0.5y_D).`

Step-by-step explanation:

When dilating a point in a plane by a factor, it involves scaling the coordinates of the point. In this case, we're dilating the quadrilateral DEFG by a factor of 0.5 with the center (0,0). The dilation affects the distance and position of each point relative to the center. For point D, if the original coordinates are
`(x_D, y_D`), after dilation, the new coordinates
`(x_D', y_D')`can be calculated using the formula for dilation:

`x_D' = k * x_D`

`y_D' = k * y_D`

Where k is the dilation factor, which here is 0.5. Therefore, the new coordinates for point D become:

`x_D' = 0.5 * x_D`

`y_D' = 0.5 * y_D`

This means that both the x-coordinate and y-coordinate of point D are halved, effectively moving it closer to the origin by a factor of 0.5 in both directions. The relative position of point D has been scaled down by half from the center of dilation.

Applying this formula to each point in the quadrilateral DEFG with their respective original coordinates will result in all the new coordinates after dilation. For point D, specifically, its position relative to the origin (0,0) has been reduced to half along both the x and y axes.