Question

regents exam questions g.srt.a.2: dilations i www.jmap.org name:
4 if △abc is dilated by a scale factor of 3, which statement is true of the image △abc?

1. 3ab = ab
2. bc = 3bc
3. m∠a = 3(m∠a)
4. 3(m∠c) = m∠c

5 the image of △abc after a dilation of scale factor k centered at point a is △ade, as shown in the diagram below.
diagram of triangle with rectangle
which statement is always true?

1. 2ab = ad
2. ad ⊥ de
3. ac = ce
4. bc || de

6 triangle klm is dilated by a scale factor of 3 to map onto triangle drs. which statement is not always true?

1. ∠k ≅ ∠d
2. km = (1/3)ds
3. the area of △drs is 3 times the area of △klm.
4. the perimeter of △drs is 3 times the perimeter of △klm.

7 a triangle is dilated by a scale factor of 3 with the center of dilation at the origin. which statement is true?

1. the area of the image is nine times the area of the original triangle.
2. the perimeter of the image is nine times the perimeter of the original triangle.
3. the slope of any side of the image is three times the slope of the corresponding side of the original triangle.
4. the measure of each angle in the image is three times the measure of the corresponding angle of the original triangle.

8 rectangle abcd is the image of rectangle abcd after a dilation centered at point a by a scale factor of 2/3. which statement is correct?

1. rectangle abcd has a perimeter that is 2/3 the perimeter of rectangle abcd.
2. rectangle abcd has a perimeter that is 3/2 the perimeter of rectangle abcd.
3. rectangle abcd has an area that is 2/3 the area of rectangle abcd.
4. rectangle abcd has an area that is 3/2 the area of rectangle abcd.

9 the perimeter of a triangle is 18. what is the perimeter of a similar triangle after a dilation with scale factor of 3?

1. 6
2. 18
3. 54
4. 162

Explanation:

Step1: Solve Q4 (Dilation side rule)

Dilation scales sides by scale factor $k=3$. So $B'C' = 3BC$. Angles are preserved, so $m\angle A'=m\angle A$, $m\angle C'=m\angle C$.

Step2: Solve Q5 (Dilation properties)

Dilation preserves parallelism. $\overline{BC} \parallel \overline{DE}$ as they are corresponding sides of similar triangles from dilation.

Step3: Solve Q6 (Dilation area rule)

Area scales by $k^2=9$, not $k=3. KM=\frac{1}{3}DS$ (since $DS=3KM$), angles are congruent, perimeter scales by $k=3$.

Step4: Solve Q7 (Dilation area rule)

Area scales by $k^2=3^2=9$. Perimeter scales by 3, slopes/angles are preserved.

Step5: Solve Q8 (Dilation perimeter rule)

Perimeter scales by scale factor $\frac{2}{3}$. Area scales by $(\frac{2}{3})^2=\frac{4}{9}$.

Step6: Solve Q9 (Dilation perimeter calculation)

New perimeter = original perimeter $\times k = 18 \times 3 = 54$.

Answer:

1. 2) $B'C' = 3BC$
2. 4) $\overline{BC} \parallel \overline{DE}$
3. 3) The area of $\triangle DRS$ is 3 times the area of $\triangle KLM$.
4. 1) The area of the image is nine times the area of the original triangle.
5. 1) Rectangle $A'B'C'D'$ has a perimeter that is $\frac{2}{3}$ the perimeter of rectangle $ABCD$.
6. 3) 54