Question

question 8
10 pts
g.gsr.3.2 (mc)
triangle abc is at a (3, 1), b (5, -2) and c (-1, -4). if the triangle is rotated 270° counter-clockwise about the origin, the translated by the rule (x+1, y - 1), what would be the coordinates of c?
○ (5, -2)
○ (-3, 0)
○ (-5, 2)
○ (-2, 2)

Explanation:

Step1: Recall 270° CCW rotation rule

The rule for rotating a point \((x, y)\) 270° counter - clockwise about the origin is \((x,y)\to(y, - x)\). For point \(C(-1,-4)\), applying the rotation rule: \(x=-1,y = - 4\), so the new coordinates after rotation \(C'\) are \((-4,1)\) (since \(y=-4\) and \(-x = -(-1)=1\)).

Step2: Apply the translation rule

The translation rule is \((x + 1,y-1)\). For the point \(C'(-4,1)\), we substitute \(x=-4\) and \(y = 1\) into the translation rule.
New \(x\) - coordinate: \(-4 + 1=-3\)
New \(y\) - coordinate: \(1-1 = 0\)

Answer:

(-3, 0)