Question

1. which is the correct algebraic representation of the transformation below?

a. $(x,y)\to(y,-x)$
b. $(x,y)\to(-y,x)$
c. $(x,y)\to(-x,y)$
d. $(x,y)\to(-x,-y)$

1. which is not a true statement about the figures shown below?

a. the image is smaller than the pre - image.
b. triangle ghi is similar to triangle $ghi$.
c. the rule $(x,y)\to(\frac{1}{3}x,\frac{1}{3}y)$ represents the transformation.
d. segment gh is congruent to segment $gh$.

Explanation:

Question 4

Step1: Analyze each transformation rule

• For rule \(A\): \((x,y)\to(y, -x)\) is a rotation of \(270^{\circ}\) counter - clockwise about the origin.
• For rule \(B\): \((x,y)\to(-y,x)\) is a rotation of \(90^{\circ}\) counter - clockwise about the origin.
• For rule \(C\): \((x,y)\to(-x,y)\) is a reflection over the \(y\) - axis.
• For rule \(D\): \((x,y)\to(-x,-y)\) is a rotation of \(180^{\circ}\) about the origin.

Looking at the figure for question 4, the transformation is a rotation (not a reflection). So the rule \((x,y)\to(-x,y)\) (reflection) is incorrect.

Step1: Analyze each statement

• Statement A: The image \(G'H'I'\) is smaller than the pre - image \(GHI\), so this statement is true.
• Statement B: Since the image is a reduction (by a scale factor), the triangles \(GHI\) and \(G'H'I'\) are similar (by the AA similarity criterion as the angles remain the same), so this statement is true.
• Statement C: If we consider a point, say \(I(0,6)\), applying the rule \((x,y)\to(\frac{1}{3}x,\frac{1}{3}y)\) gives \(I'(0,2)\). For \(G(- 3,-3)\), applying the rule gives \(G'(-1,-1)\) and for \(H(3,-3)\) gives \(H'(1,-1)\). So this rule represents the transformation (a dilation), and this statement is true.
• Statement D: Since the image is a reduction (by a scale factor of \(\frac{1}{3}\)), \(GH

eq G'H'\) (if \(GH\) has length \(6\) (distance between \((-3,-3)\) and \((3,-3)\) is \(|3 - (-3)|=6\)), \(G'H'\) has length \(2\) (distance between \((-1,-1)\) and \((1,-1)\) is \(|1-(-1)| = 2\)). So this statement is false.

Answer:

C

Question 5