Question

question 1
what transformation maps triangle abc to triangle abc
in the image?
reflection over the y - axis
rotation 90° clockwise
dilation with scale factor 2
translation 3 units right

Explanation:

Step1: Analyze reflection over y - axis

Reflection over the y - axis changes the x - coordinate sign. For example, if a point is \((x,y)\), its reflection is \((-x,y)\). But in the image, the x - coordinates of the corresponding points (e.g., \(A(1,1)\) and \(A'(4,1)\)) do not follow this rule.

Step2: Analyze rotation 90° clockwise

Rotation 90° clockwise changes a point \((x,y)\) to \((y,-x)\). For example, if \(C(2,3)\), after rotation 90° clockwise, it should be \((3,-2)\), which is not the case in the image.

Step3: Analyze dilation with scale factor 2

Dilation with scale factor \(k\) changes a point \((x,y)\) to \((kx,ky)\). If \(k = 2\), for \(A(1,1)\), it should be \((2,2)\), which is not the case in the image.

Step4: Analyze translation 3 units right

Translation 3 units right changes a point \((x,y)\) to \((x + 3,y)\). For \(A(1,1)\), \(1+3=4\), so \(A'(4,1)\); for \(B(3,1)\), \(3 + 3=6\), so \(B'(6,1)\); for \(C(2,3)\), \(2+3 = 5\), so \(C'(5,3)\). This matches the coordinates in the image.

Answer:

Translation 3 units right