Question

30 points, real good help please.

- Create your own set of coordinates for and graph it on a coordinate plane.
- Write a scenario involving the dilation of ABC onto its image. In the scenario, include the scale factor between the similar triangles and the coordinates for the image.
- Use the distance formula or Pythagorean Theorem to prove mathematically that is similar to its image. Include all necessary calculations.

Answer 1

We choose the coordinates (4,4), (4,10), and (8,4) as the vertices of right-angle triangle ABC We want to dilate triangle ABC by scale factor of 2 at the center (0,2)The image is shown below as triangle A'B'C' with coordinates (8.6), (8,18), and (18,6). Triangle ABC has a base of 4 units and a height of 6 units

Triangle A'B'C' has a base of 8 units and a height of 12 unitsApplying Pythagoras theorem to triangle ABC to find the hypotenuse

Now, we calculate the hypotenuse of the image

The hypotenuse of the image is twice the hypotenuse of triangle ABC which proof the two shapes are similar shape