Question

which is not a true statement about the figures shown below?○ the image is smaller than the pre-image.○ triangle ghi is similar to triangle ghi.○ the rule (x, y) → (1/3x, 1/3y) represents the transformation.○ segment gh is congruent to segment gh.

Explanation:

Step1: Identify coordinates of points

Pre-image (△GHI): $G(-3, -3)$, $H(3, -3)$, $I(0, 6)$
Image (△G'H'I'): $G'(-1, -1)$, $H'(1, -1)$, $I'(0, 2)$

Step2: Analyze each option

Option1: Image vs pre-image size

Pre-image side GH length: $|3 - (-3)| = 6$
Image side G'H' length: $|1 - (-1)| = 2$. $2<6$, so image is smaller. True

Option2: Similarity check

Check side ratios:
$\frac{G'H'}{GH}=\frac{2}{6}=\frac{1}{3}$, $\frac{I'G'}{IG}=\frac{\sqrt{(-1-0)^2+(-1-2)^2}}{\sqrt{(-3-0)^2+(-3-6)^2}}=\frac{\sqrt{1+9}}{\sqrt{9+81}}=\frac{\sqrt{10}}{\sqrt{90}}=\frac{1}{3}$, $\frac{I'H'}{IH}=\frac{1}{3}$. All ratios equal, so triangles are similar. True

Option3: Verify transformation rule

Apply $(x,y)\to(\frac{1}{3}x,\frac{1}{3}y)$ to pre-image:
$G(-3,-3)\to(\frac{1}{3}(-3),\frac{1}{3}(-3))=(-1,-1)=G'$
$H(3,-3)\to(\frac{1}{3}(3),\frac{1}{3}(-3))=(1,-1)=H'$
$I(0,6)\to(\frac{1}{3}(0),\frac{1}{3}(6))=(0,2)=I'$. Rule matches. True

Option4: Congruence of GH and G'H'

$GH=6$, $G'H'=2$. $6
eq2$, so segments are not congruent. False

Answer:

Segment GH is congruent to segment G'H'.