Sovi AI

Pregunta

Pasos de solución

1. Understand the question

   Turn 1 Question

   which sequence of transformations maps a rectangle from (1,2), (1,4), (3,4), and (3,2) to (-2,-4), (-2,-8), (-6,-8), and (-6,-4)?

   a. translation by 9 units left and 12 units down
   b. translation by 2 units right
   c. dilation by scale factor of -2
   d. dilation by scale factor of 2

   Turn 2 Question

   Which transformation does not preserve the size of a figure? a. Reflection b. Rotation c. Dilation d. Translation

2. Response

   Turn 1 Answer

3. Explanation

   Step1: Pick a reference point

   Take the point $(1,2)$ and its image $(-2,-4)$.

   Step2: Test dilation factor

   Check scaling: $1 \times k = -2$ and $2 \times k = -4$. Solve for $k$: $k = \frac{-2}{1} = -2$, $k = \frac{-4}{2} = -2$.

   Step3: Verify with another point

   Test $(1,4)$: $1 \times (-2) = -2$, $4 \times (-2) = -8$, which matches $(-2,-8)$.

   Step4: Eliminate other options

   Translation would add/subtract constants, not scale coordinates. Scale factor 2 would give positive values, not negative.

4. Brief Explanations

   Reflections, rotations, and translations are rigid transformations—they only change the position or orientation of a figure, keeping its side lengths, angles, and overall size identical. Dilation involves scaling a figure by a factor (other than 1), which increases or decreases its linear dimensions, thus changing its size.

5. Final answer

   c. dilation by scale factor of -2

   Turn 2 Answer

Respuesta

Question Analysis

OCR Text

Which transformation does not preserve the size of a figure? a. Reflection b. Rotation c. Dilation d. Translation

Temas relacionados

Preguntas relacionadas

• use an area model to solve 31 × 26. multiply in the area model.

  Top-left cell: 180 Top-right cell: 6 Bottom-left cell: 600 Bottom-right cell: 20 Final product: 806

• 6. solve each equation. write each solution as a fraction and as a deci…

  | Equation | Solution (Fraction) | Solution (Decimal) | |----------|---------------------|--------------------| | $2x=3$ | $\frac{3}{2}$ | $1.5$ | | $5y=3$ | $\frac{3}{5}$ | $0.6$…

• Ok

  - Fila 2: Circular el par (5, 2). - Fila 3: Circular el par (3, 3) (o la tarjeta con 3 y la otra con 4 dibujos, pero los números son 3 y 3? Wait, la tercera fila: primera tarjeta …

• How do you solve pemdas

  It's basically just a checklist so you don't get mixed up when a math problem has a bunch of stuff going on at once. You just go down the list in order: 1. **P**arentheses: Do any…

• which number line models $-1 + (-14)$? add. $-1 + (-14) = \\square$

  \(-15\)

• 11 et 12

  The initial number of bacteria is 5. ### Turn 2 Answer Ça marche, regardons ça ! On dirait que tu es en plein dans les maths financières. Pour le **numéro 11**, on cherche le taux…

• if a figure is rotated 90 degrees clockwise, what happens to a point at…

  b. It moves to (2,−3).

• a figure is rotated 180 degrees around the origin and then dilated by a…

  d. (6,−8)

Sovi AI iOS

Sitio oficial: mysovi.ai. Las páginas se sirven en question-banks.mysovi.ai. La app iOS está en Apple App Store.