Question

the graph shows trapezoids abcd and abcd. which of the following transformations maps abcd onto abcd? translation left 4 units and down 9 units translation left 5 units and down 10 units reflection across the x - axis reflection across the y - axis rotation 90° clockwise around the origin rotation 90° counterclockwise around the origin rotation 180° around the origin

Explanation:

Step1: Analyze translation

Check the change in x - and y - coordinates of corresponding points. For point A(7,9) and A'(2,0), the change in x is \(7 - 2=5\) (left 5 units) and the change in y is \(9-0 = 9\) (down 9 units). This does not match the given translation options.

Step2: Analyze reflection across x - axis

If we reflect a point \((x,y)\) across the x - axis, the new point is \((x,-y)\). For example, if we take point A(7,9), its reflection across the x - axis would be (7, - 9), which is not A'(2,0).

Step3: Analyze reflection across y - axis

If we reflect a point \((x,y)\) across the y - axis, the new point is \((-x,y)\). For point A(7,9), its reflection across the y - axis would be (-7,9), which is not A'(2,0).

Step4: Analyze 90° clockwise rotation

The rule for a 90° clockwise rotation around the origin is \((x,y)\to(y,-x)\). For point A(7,9), it would become (9, - 7), which is not A'(2,0).

Step5: Analyze 90° counter - clockwise rotation

The rule for a 90° counter - clockwise rotation around the origin is \((x,y)\to(-y,x)\). For point A(7,9), it would become (-9,7), which is not A'(2,0).

Step6: Analyze 180° rotation

The rule for a 180° rotation around the origin is \((x,y)\to(-x,-y)\). For point A(7,9), \(x = 7,y = 9\), and \((-x,-y)=(-7,-9)\). For point B(5,9), \((-x,-y)=(-5,-9)\), for point C(5,6), \((-x,-y)=(-5,-6)\) and for point D(7,6), \((-x,-y)=(-7,-6)\). This is not correct.
Let's re - check translation. For point A(7,9) and A'(2,0), the correct translation is left 5 units (\(7-2 = 5\)) and down 9 units (\(9 - 0=9\)).

Answer:

translation left 5 units and down 9 units