Question

1. point a at (7, -8) is rotated 270° clockwise about the origin to create point a. bella thinks point a will be located at (-8, 7). ben thinks point a will be located at (8, 7). who is correct and why?

Explanation:

Step1: Recall rotation rule

When a point \((x,y)\) is rotated \(270^{\circ}\) clockwise about the origin, the new coordinates \((x',y')\) follow the rule \((x,y)\to(y,-x)\).

Step2: Apply the rule to point \(A(7,-8)\)

Here \(x = 7\) and \(y=-8\). Using the rule \((x,y)\to(y,-x)\), we substitute \(x = 7\) and \(y = - 8\) into the formula. So \(x'=-8\) and \(y'=7\).

Answer:

Bella is correct. When a point \((x,y)\) is rotated \(270^{\circ}\) clockwise about the origin, the transformation rule is \((x,y)\to(y,-x)\). For point \(A(7,-8)\), applying the rule gives \(A'(-8,7)\) which is what Bella thought.