Question

13/19
place the image of points a, b, and c after a rotation of \\( \triangle abc 270 ^ { \circ } \\) around the origin. \\( ( 0,0 ) \\)
перетащите метки в правильное положение на изображении.
point \\( c ^ { \prime } \\) point \\( b ^ { \prime } \\) point \\( a ^ { \prime } \\)

Explanation:

Step1: Determine the coordinates of original points

Assume \(A(-4,-4)\), \(B(4,-1)\), \(C(6,-6)\)

Step2: Apply the rotation formula

The formula for a \(270^{\circ}\) rotation about the origin \((x,y)\to(y, -x)\)
For point \(A(-4,-4)\):
Substitute \(x = - 4\), \(y=-4\) into \((y,-x)\)
\(A'(-4,4)\)
For point \(B(4,-1)\):
Substitute \(x = 4\), \(y = - 1\) into \((y,-x)\)
\(B'(-1,-4)\)
For point \(C(6,-6)\):
Substitute \(x = 6\), \(y=-6\) into \((y,-x)\)
\(C'(-6,-6)\)

Answer:

Point \(A'\) should be placed at \((-4,4)\), Point \(B'\) at \((-1,-4)\) and Point \(C'\) at \((-6,-6)\)