Question

If you draw the image of this figure which has coordinates A= (1,6) B=(1,9) C= (2,9) and D= (3,7) under a 90 degree clockwise rotation using the point outside of the shape as the center what will be the 4 coordinates points of the new figure

Answer 1

The new coordinates after a 90-degree clockwise rotation around a point outside the shape can be determined by subtracting the rotation center from each point, applying the rotation transformation, and then adding the rotation center back.

Step-by-step explanation:

In order to find the new coordinates after a 90-degree clockwise rotation about a point outside the shape, we apply the following steps to each original coordinate (x, y):

Subtract the x and y values of the rotation center from the original coordinate.

Apply the 90-degree clockwise rotation transformation, which switches the x and y values and changes the sign of the new y value.

Add the x and y values of the rotation center back to the transformed coordinate.

To demonstrate with an example, let's assume the center of rotation is at point P (px, py).

For a point A (1,6), the steps are as follows:

A - P = (1 - px, 6 - py)

Apply rotation: the new point A' will be (6 - py, -(1 - px))

A' + P = (6 - py + px, py - (1 - px)) = (6 + px - py, py - 1 + px)

Repeat this process for points B, C, and D to find their new coordinates after the rotation.