Question

coordinate moves

1. rotate segment ab 90 degrees clockwise around (0, 0). label the image of a as e and the image of b as f. what are the coordinates of e and f?

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree clockwise rotation about the origin \((0,0)\) for a point \((x,y)\) is \((x,y)\to(y, - x)\).

Step2: Assume coordinates of B

Let the coordinates of point \(B\) be \((x_1,y_1)\). After a 90 - degree clockwise rotation about the origin, the image of \(B\) (say \(F\)) has coordinates \((y_1,-x_1)\). And assume we know some information about the pre - image \(B\) to calculate the exact coordinates of \(F\). Also, if we have another point \(E\) with pre - image coordinates \((x_2,y_2)\), its 90 - degree clockwise rotated image coordinates will be \((y_2,-x_2)\) according to the rotation rule.

Answer:

Without the original coordinates of \(B\), \(E\), we cannot give specific numerical answers. But if the coordinates of \(B=(x,y)\), the coordinates of its 90 - degree clockwise rotated image \(F\) are \((y, - x)\) and for a point \(E=(m,n)\), its 90 - degree clockwise rotated image has coordinates \((n,-m)\)