Question

question 1
5 points
which transformation sequence preserves size and shape?
dilate by a factor of 1/2, then rotate 90°
reflect over y-axis, then translate 5 units right
translate 4 units left and then stretch vertically by a factor of 3
reflect over the y-axis and then resize
question 2
5 points
point e(1, -4) is translated 2 units left and 3 units up, then
rotated 180° around the origin. what are the final
coordinates?
(-1,1)
(3, -7)
(1,1)
(-1, -1)
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question 3

Explanation:

Question 1

Step1: Analyze dilation

Dilation changes the size. If we dilate by a factor of \(1/2\), the size changes. So the first option is wrong.

Step2: Analyze reflection and translation

Reflection over \(y\) - axis and translation (shifting) are rigid transformations. Rigid transformations (reflection, translation, rotation) preserve size and shape. Reflecting over \(y\) - axis and then translating 5 units right is a combination of rigid transformations.

Step3: Analyze stretching

Stretching (vertical stretch by a factor of 3) changes the size. So the third option is wrong.

Step4: Analyze resizing

Resizing changes the size. So the fourth option is wrong.

Question 2

Step1: Translation

For a point \((x,y)\), translating 2 units left (subtract 2 from \(x\)) and 3 units up (add 3 to \(y\)).
Given \(E(1,-4)\), after translation: \(x = 1-2=-1\), \(y=-4 + 3=-1\). The point becomes \((-1,-1)\)

Step2: Rotation

The rule for a \(180^{\circ}\) rotation around the origin is \((x,y)\to(-x,-y)\).
For the point \((-1,-1)\), after rotation: \(x=-(-1) = 1\), \(y=-(-1)=1\)

Answer:

• Question 1: Reflect over \(y\) - axis, then translate 5 units right
• Question 2: \((1,1)\)