Question

3 multiple choice 4 points which of the following will map △abc onto △abc? translation 2 units right and 1 unit up clockwise turn 90° about the origin reflection in the y - axis reflection in the x - axis 4 multiple choice 4 points refer to the figure below. if the triangle is reflected across the x - axis, the coordinates of the new vertices will be (1, - 1), (3, - 3), and __________.

Explanation:

Step1: Analyze translation

Translation 2 units right and 1 unit up would change the \(x\) - coordinate by adding 2 and \(y\) - coordinate by adding 1. But this does not map \(\triangle ABC\) to \(\triangle A'B'C'\).

Step2: Analyze 90 - degree clockwise rotation

For a clock - wise 90 - degree rotation about the origin, the transformation rule for a point \((x,y)\) is \((y, - x)\). This does not map \(\triangle ABC\) to \(\triangle A'B'C'\).

Step3: Analyze y - axis reflection

For reflection in the \(y\) - axis, the transformation rule for a point \((x,y)\) is \((-x,y)\). This does not map \(\triangle ABC\) to \(\triangle A'B'C'\).

Step4: Analyze x - axis reflection

For reflection in the \(x\) - axis, the transformation rule for a point \((x,y)\) is \((x,-y)\). If we consider the vertices of \(\triangle ABC\) and apply this rule, we can map \(\triangle ABC\) onto \(\triangle A'B'C'\).

Answer:

reflection in the \(x\) - axis