Question

a dilation (1 point) Quadrilateral ABCD has been translated units to the right and units down.
A(2,2) B(4,6) C(4,10) D(2,6) Quadrilateral ABCD has been translated what units to the right and what units down? new coordinates are H(1,15) E(11,1) G(1,19) F(15,1)

Answer 1

To find the translation of quadrilateral ABCD, we first need to determine the change in the x-coordinates and the change in the y-coordinates based on the original coordinates of the quadrilateral ABCD and the new coordinates H, E, G, F.

The original coordinates are:
- A(2, 2)
- B(4, 6)
- C(4, 10)
- D(2, 6)

The new coordinates after the translation are:
- H(1, 15)
- E(11, 1)
- G(1, 19)
- F(15, 1)

To determine the translation, we can check how the original points have changed to become the new points.

For point A(2, 2) to H(1, 15):
- Change in x: 1 - 2 = -1 (translated 1 unit to the left)
- Change in y: 15 - 2 = 13 (translated 13 units up)

For point B(4, 6) to E(11, 1):
- Change in x: 11 - 4 = 7 (translated 7 units to the right)
- Change in y: 1 - 6 = -5 (translated 5 units down)

For point C(4, 10) to G(1, 19):
- Change in x: 1 - 4 = -3 (translated 3 units to the left)
- Change in y: 19 - 10 = 9 (translated 9 units up)

For point D(2, 6) to F(15, 1):
- Change in x: 15 - 2 = 13 (translated 13 units to the right)
- Change in y: 1 - 6 = -5 (translated 5 units down)

From the changes in coordinates, we can see that the translations vary for each point. Therefore, it is not a uniform translation for the entire shape.

Instead, we can summarize the translations made:
- A to H: 1 unit left, 13 units up
- B to E: 7 units right, 5 units down
- C to G: 3 units left, 9 units up
- D to F: 13 units right, 5 units down

Thus, there is no single translation applied uniformly to quadrilateral ABCD; rather, each point has undergone a different translation.